[edit]
The following applies to all carriers except for BA inbound flights it seems!
[/edit]
You clear immigration then
collect your luggage before clearing customs.
Just after customs is a bag recheck are where you redeposit your luggage before heading though priority security (being in F) back airside.
If all goes well, your CUN flight would have commenced boarding by then.
(BTW, are you sure your CUN flight is in First ... not Business?)