\[ \int_0^1 ( \{ 2x \} - 1)(\{ 3x \} - 1) \, dx \]

If the value of the integral above equals \( \dfrac AB\), where \(A\) and \(B\) are coprime positive integers, find \(A+B\).

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

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