Who's up to the challenge? 6

Calculus Level 5

\[ \large \displaystyle\int _{ 0 }^{ \infty }{ { e }^{ -{ x }^{ 3 } }\sin { { x }^{ 3 } } \, dx } =\dfrac { (\sqrt { A } -1)\Gamma (\frac { B }{ C } ) }{ \sqrt [ 3 ]{ { D }^{ E } } } \]

If the equation above holds true for positive integers \(A,B,C,D\) and \(E\), find the minimum value of \(A+B+C+D+E\).


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