Definite Integral is not hard!

Calculus Level 4

The value of

\[\int_0^{\infty}\frac{x}{(1 + x^3)^2} dx \]

can be expressed as \(\frac {\pi a \sqrt{b}}{c},\) where \(a\) and \(c\) are coprime and \(b\) is square-free. Find the value of the sum \(a+b+c.\)

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