Resembling Resemblence-3

Calculus Level 5

\[\large\displaystyle\int_0^\infty \log \dfrac{1+x^3}{x^3} \dfrac{x \,dx}{1+x^3}=\dfrac{\pi}{\sqrt M}\log M-\dfrac{\pi^N}{M^2}.\]

The equation above is true for \(M\) and \(N\) are positive integers. Find \(M+N\).

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