I've been looking around and I got that the three words can mean "future". Is there a way to differentiate them? Can they be used the same way?
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未来 and 将来 are pretty similar to each other. 大辞泉 breaks down the differences under the 用法 section of 「将来」 entry (explanation translated):
To summarize: they're very similar, but when used as an adverb, it's almost invariably 将来, not 未来, and 未来 by default has a farther-off, less tangible connotation.
As for 行く末, it's less common and seems to me to be a more personal sort of future. But I'd stick with 将来 and 未来 for almost all contexts.
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Literally they should roughly mean:
将来 - That which is about to come
未来 - That which has not yet come
This corresponds to the other answers here that indicates that