\[\large \int _{ 0 }^{ 1 }{ \left\{ \dfrac { 1 }{ { x }^{1/6 } } \right\} \,dx } =\dfrac { A }{ B } -\dfrac { { \pi }^{ C } }{ D } \]

The equation above holds true for positive integers \(A,B,C\) and \(D\), with \(A,B\) coprime. Find \(A+B+C+D\).

**Notation**: \( \{ \cdot \} \) denotes the fractional part function.

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