Seven seas in this world!

Calculus Level 4

\[ \large \int_0^\infty \dfrac{x^7}{1-e^x} \, dx\]

If the integral above is equal to \( -\dfrac AB \pi^C\), where \(A,B\) and \(C\) are coprime positive integers with \(A,B\) coprime, find \(A+B+C\).

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