Problematic Combinations

The number of ways in which the number 2160 can be written as \(abc\) where \(a\), \(b\) and \(c\) are positive integers is X and the number of ways in which 2160 can be written as \(d + e + f\) where \(d\), \(e\) and \(f\) are positive integers is Y. Find X + Y.

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