Three three three

Calculus Level 5

\[\int_1^\infty\int_0^\infty\dfrac{1}{(x^3+y^3)^3}dx\text{ }dy=\dfrac{A\pi\sqrt{B}}{C}\]

Given that \(A,B\) and \(C\) are integers satisfying the equation above, find \(A+B+C\).


This integral was shared with me by a friend, who saw the integral on Mathematics Stack Exchange.
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