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RETIREMENT PLANS - Narrative (Details) | 6 Months Ended |
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Apr. 13, 2025 healthcarePlan definedBenefitPensionPlan | Jan. 01, 2022 USD ($)
Retirement Benefits [Abstract] |  |
Number of sponsored defined benefit pension plans | definedBenefitPensionPlan | 2 |
Number of postretirement health care plans | healthcarePlan | 2 |
Minimum required contribution for retirement plans | $ |  | $ 0

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- Definition Minimum required contribution for retirement plans + References No definition available. + Details
Name: | jack_MinimumRequiredContributionForRetirementPlans
Namespace Prefix: | jack_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

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- Definition Number Of Defined Benefit Pension Plans Sponsored + References No definition available. + Details
Name: | jack_NumberOfDefinedBenefitPensionPlansSponsored
Namespace Prefix: | jack_
Data Type: | xbrli:integerItemType
Balance Type: | na
Period Type: | duration

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- Definition Postretirement Medical Plan, Number Sponsored + References No definition available. + Details
Name: | jack_PostretirementMedicalPlanNumberSponsored
Namespace Prefix: | jack_
Data Type: | xbrli:integerItemType
Balance Type: | na
Period Type: | duration

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- References No definition available. + Details
Name: | us-gaap_CompensationAndRetirementDisclosureAbstract
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration