Who's up to the challenge? 56

Calculus Level 5

$\large \int _{ -\infty }^{ \infty }{ \dfrac { \ln { (1+{ e }^{ 2x } } ) }{ 1+{ e }^{ 3x } } \, dx } =\frac { A\pi ^{ C } }{ B }$

If the equation above holds for coprime positive integers $$A,B$$ and an integer $$C$$, then find $$A+B+C$$.

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