You sure about AM about that? AeroMexico only serves CVG via their codeshare, and the daily flight on CVG-CUN is a DL 738.

@Boraxo:
If you were willing to forego FC on your trip to CUN, SLC might also be a connection opportunity. Fly SFO-SLC onboard an ASA CR7, and connect to the 738 to CUN. Ways are short in SLC, and except in the late afternoon it is also usually not that full.
If you choose to go FC via ATL, be prepared to fly a red-eye. And depending on the day, you have 5 flight options on ATL-CUN, 3x DL and 2x AM.