Always check the Monitors....ALWAYS
First, sorry you missed your flight.
You're in MIA, ALWAYS-ALWAYS-ALWAYS keep checking the monitors for last minute gate changes. How many times are you on the plane and you hear after the FA announces the connecting gates, to ALWAYS double check the monitors because GATE CHANGES happen often and without notice.
Utilize the SKYTRAIN, it is actually FASTER than walking from one end of the concourse to the other end. Trains do depart approximately every 2 minutes.
NEVER trust the gate info on a boarding pass you printed at home. Again, your in MIA and changes happen often.
Always listen to the announcements in the terminal, they could be announcing a Gate Change for YOUR flight.