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Nicki Minaj and Meek Mill broke up after a nuclear fight during her birthday weekend last month ... and it wasn't about cheating.

Sources close to the ex-couple tell us ... they weren't getting along in Turks and Caicos, because he was hanging with friends and not paying attention to her. She went nuts on him, he got pissed and left the island without her, and she said, "Screw this," and ended the relationship. Just that simple.