\[\large \int _{ 0 }^{ \infty }{ \frac { { x }^{ 3 } }{ { e }^{ 2x }-{ e }^{ 3x } } dx } \]

If the value of the integral above is equal to

\[ -\dfrac{\pi^A}B + \dfrac CD\]

where \(A,B,C\) and \(D\) are positive integers with \(C,D\) coprime, find \(A+B+C+D\).

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