B727 LNDG MIA EXPERIENCED CONFLICT WITH A DEP WHEN UNABLE TO EXIT RWY AS ATC DIRECTED.

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ON LNDG ROLLOUT AND AFTER FO XFERRED CTL TO CAPT; MIA TWR CLRED US TO L TURN (TO EXIT RWY); CROSS RWY 8 AND TAXI TO RAMP. WE ATTEMPTED TO TURN OFF AT TXWY L6; BUT SAW BARRELS ON TXWY; SO WE CONTINUED TO TXWY L7; WHILE HEARING THAT ACR Y WAS CLRED FOR TKOF BY TWR (BUT NOT INDICATING WHICH RWY THEY WERE ON). APCHING TXWY L7; WE SAW BARRELS ON THAT TXWY ALSO. SO I; (FO); ADVISED TWR THAT WE WERE UNABLE TO TURN THERE AND ASKED FOR ASSISTANCE. TWR INSTRUCTED ACR Y TO CANCEL TKOF CLRNC. OUR FE SAID WE NEEDED TO GET OFF IMMEDIATELY AND THE CAPT WENT FOR THE CLOSED TXWY L7. TWR AGAIN REQUESTED ACR Y TO CANCEL TKOF CLRNC AND INSTRUCTED US TO CLR RWY IMMEDIATELY. WE DID; EXITING AT TXWY L7; STOPPING PRIOR TO THE BARRELS AND CLRING OUR TAIL JUST AS THE ACR Y TOOK OFF AND CLRED US BY APPROX 50 FT HORIZ AND 75 FT VERT. WE WERE NOT SURE WHEN THE ACR Y WAS GIVEN THE AMENDMENT TO CANCEL THEIR TKOF DURING THEIR ROLL; BUT IT MAY HAVE BEEN TOO LATE TO STOP IN TIME AND THEY MAY HAVE HAD TO CONTINUE THE TKOF AS THE ONLY SAFE OPTION. THEY PROBABLY HAD TO LIFT OFF EARLY TO AVOID A POSSIBLE INCURSION. IF NOT FOR ALL 3 OF OUR CREW MEMBERS ACTIONS AND THE ACTIONS OF ACR Y; WE WOULD HAVE HAD AN ACCIDENT. THERE WAS NO INFO GIVEN TO US ON TXWY CLOSURES BY ATC; ATIS NOR NOTAMS. IF WE HAD THAT; WE COULD HAVE ROLLED IMMEDIATELY TO EXIT AT AN OPEN TXWY. ALSO; WE NEVER LEFT THE RWY PRIOR TO GIVEN THE INSTRUCTION TO EXIT IMMEDIATELY -- WHICH WE DID AT THE CLOSED TXWY; INDICATED BY THE BARRELS. ATC SHOULD HAVE NOT CLRED THE OTHER ACFT TO TAKE OFF UNTIL WE WERE OFF THE RWY. AFTER THIS HAPPENED AND DURING TAXIING TO RAMP; TWR ASKED THE GND TRUCK WHICH TXWYS WERE BLOCKED. I DO NOT THINK TWR KNEW EITHER THAT THOSE TXWYS WERE BLOCKED.