\[ \large \int_0^1 \int_0^1 \left \{ \dfrac {x^3}y \right \} \, dx \: dy = \dfrac AB - \dfrac \gamma C \]

If the equation above holds true for positive integers \(A\), \(B\) and \(C\), with \(A\), \(B\) coprime, find \(A+B+C\).

**Notations**:

- \( \{ \cdot \} \) denotes the fractional part function.
- \(\gamma \approx 0.5772 \) denotes the Euler-Mascheroni constant.

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