66 minutes is NOT enough time to connect from DL to AA in MIA. It is enough to connect between an AA domestic flight to an AA international flight
ETA: 66 minutes is also a tight connection IMHO - even is AA to AA. I'd be more comfortable with a minimum of a 90 minute connection in MIA.
YMMV
Sorry, should have included it in OP. It would be DL to LA connection, both of which operate from terminal H.
I get general impression that I shouldn't get cute and just book AA flight which would give an extra hour to connect.