Who's up to the challenge? 62

Calculus Level 5

\[\int _{ 0 }^{ 1 }{ \int _{ 0 }^{ 1 }{ \dfrac { (\ln { } { xy })^4 }{ (1+xy)^{ 2 } }\, dx \; dy } } =\dfrac { A }{ B } \zeta (C)\]

If the equation above holds true for positive integers \(A,B\) and \(C\), where \(A\) and \(B\) are coprime, find \(A+B+C\).

\[\]Notation: \(\zeta(\cdot) \) denotes the Riemann zeta function.

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