Let's integrate 2

Calculus Level 2

\[\displaystyle \int \dfrac{x^3}{\sqrt[3]{1+x^4}} dx\]

If the value of above expression is in the form \(\frac{A}{B}\sqrt[X]{(1+x^4)^{Y}}+C\), where \(A,B,X,Y\) are positive integers with \(\gcd(A,B) = \gcd(X,Y) = 1\), find \(A+B+X+Y\).

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