Hot Integrals

Calculus Level 4

\[\large \int_{0}^{\infty }\dfrac{dx}{1+x^{3}}\]

If the value of the integral above can be expressed in the form \[\dfrac{A \sqrt B}C \pi, \] where \(A,B,C\) are positive integers with \(A,C\) coprime and \(B\) square-free, find \(A+B+C\).

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