Segment Information - Disaggregation of Revenue (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Sep. 28, 2025	Sep. 29, 2024	Sep. 28, 2025	Sep. 29, 2024
Disaggregation of Revenue [Line Items]
Total revenues	$ 508,154	$ 506,807	$ 1,555,629	$ 1,528,617
Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	168,421	171,097	521,291	546,988
Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	47,051	45,830	143,409	139,535
Commissary sales
Disaggregation of Revenue [Line Items]
Total revenues	229,581	228,989	693,098	660,823
Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	21,424	19,521	68,317	60,866
Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	41,677	41,370	129,514	120,405
Operating segments
Disaggregation of Revenue [Line Items]
Total revenues	504,362	505,064	1,539,698	1,520,965
Operating segments | Domestic Company-Owned Restaurants
Disaggregation of Revenue [Line Items]
Total revenues	165,194	168,672	511,786	518,103
Operating segments | Domestic Company-Owned Restaurants | Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	165,194	168,672	511,786	518,103
Operating segments | Domestic Company-Owned Restaurants | Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | Domestic Company-Owned Restaurants | Commissary sales
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | Domestic Company-Owned Restaurants | Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | Domestic Company-Owned Restaurants | Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | North America Franchising
Disaggregation of Revenue [Line Items]
Total revenues	34,958	34,842	108,372	107,038
Operating segments | North America Franchising | Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | North America Franchising | Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	34,958	34,842	108,372	107,038
Operating segments | North America Franchising | Commissary sales
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | North America Franchising | Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | North America Franchising | Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | North America Commissaries
Disaggregation of Revenue [Line Items]
Total revenues	259,489	262,452	791,524	763,506
Operating segments | North America Commissaries | Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | North America Commissaries | Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | North America Commissaries | Commissary sales
Disaggregation of Revenue [Line Items]
Total revenues	259,489	262,452	791,524	763,506
Operating segments | North America Commissaries | Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | North America Commissaries | Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Operating segments | International
Disaggregation of Revenue [Line Items]
Total revenues	44,721	39,098	128,016	132,318
Operating segments | International | Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	3,227	2,425	9,505	28,885
Operating segments | International | Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	13,254	12,000	38,701	35,598
Operating segments | International | Commissary sales
Disaggregation of Revenue [Line Items]
Total revenues	20,178	18,600	55,930	48,950
Operating segments | International | Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	3,278	2,789	9,971	9,641
Operating segments | International | Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	4,784	3,284	13,909	9,244
All Other
Disaggregation of Revenue [Line Items]
Total revenues	68,866	68,289	216,958	202,808
All Other | Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
All Other | Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
All Other | Commissary sales
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
All Other | Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	22,463	20,247	71,842	61,924
All Other | Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	46,403	48,042	145,116	140,884
Elimination of Intersegment Revenue
Disaggregation of Revenue [Line Items]
Total revenues	(65,074)	(66,546)	(201,027)	(195,156)
Elimination of Intersegment Revenue | Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	0	0	0	0
Elimination of Intersegment Revenue | Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	(1,161)	(1,012)	(3,664)	(3,101)
Elimination of Intersegment Revenue | Commissary sales
Disaggregation of Revenue [Line Items]
Total revenues	(50,086)	(52,063)	(154,356)	(151,633)
Elimination of Intersegment Revenue | Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	(4,317)	(3,515)	(13,496)	(10,699)
Elimination of Intersegment Revenue | Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	$ (9,510)	$ (9,956)	$ (29,511)	$ (29,723)