POTENTIAL CONFLICT WITH LTSS NOT RESOLVED IN OPPOSITE DIRECTION TFC INCIDENT. CLB THROUGH OCCUPIED ALT WHEN XING RESTRICTION NOT MET. ALTDEV ALT UNDERSHOT.

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WE DEPARTED SANTO DOMINGO AT XY46Z ON THE KODIX 2 DEP. PASSING FL220 WE WERE ASKED BY SANTO DOMINGO ACC (124.3) TO CROSS 15 DME SE OF PUERTO PLATA VOR AT OR ABOVE FL350. WE WERE CLRED TO FL390. WE STATED 3 TIMES THAT WE WERE UNABLE TO COMPLY WITH THIS CLRNC. DURING RADIO EXCHANGES WE WERE TOLD THE CONFLICTING TFC WAS EXPECTED TO CROSS PUERTO PLATA VOR AT XX07Z AT FL330. NUMEROUS OTHER ACFT WERE ON THE FREQ AND COMS WERE OCCURRING IN BOTH SPANISH AND ENGLISH. THE CTLR DID NOT RESPOND TO OUR BEING UNABLE TO CROSS 15 DME S OF PTA AT FL350. WE EXPECTED AN ALT CHANGE OR RERTE OR A CHANGE IN CLRNC FOR THE OTHER ACFT. NONE OF THIS HAPPENED AND WE COULD NOT GET A WORD IN ON THE FREQ TO QUESTION THE CTLR. AT XX01Z WE HEARD ANOTHER ACR ON THE FREQ ASKING ABOUT AN OBSERVED (VISUAL OR TCASII??) ACFT AT OUR POS AND ALT. AT XX02; 17 DME SE OF PUERTO PLATA WE OBSERVED THE ACR Y ACFT PASSING TO OUR R AS WE CLBED THROUGH FL335. BOTH ACFT ACKNOWLEDGED ON 124.3. PTA ACC (CTR) THEN RESPONDED THAT THEY DID NOT KNOW WE HAD STATED THAT WE WERE UNABLE TO COMPLY WITH THEIR XING REQUEST. WE WERE ON A-554 AND ACR Y WAS SBOUND ON W-2; A NEARBY AIRWAY OUT OF PTA. NO FURTHER APPLICABLE STATEMENTS BY PTA CTR OR ACR Y WERE MADE. THIS PROBLEM WAS CAUSED BY AN OVERWORKED CTLR; A NON-RADAR ENVIRONMENT WITH JETS; AND LANGUAGE DIFFICULTIES.