AA 1153 then DL 598 at Atlanta
Chicago O'Hare → Atlanta → Cancún
Timetable, Atlanta time
11:05AA 1153 from Chicago O'Hare at the gate
11:02DL 598 to Cancún leaves the gate
23 h 57 apart on the timetable, overnight
DL 598 leaves 23 h 57 after AA 1153 arrives on the timetable: more than half a day, so not a connection we count.