$\large \displaystyle\int _{ 0 }^{ 1 }{ \left\{ \dfrac { 1 }{ { x }^{ 1729 } } -\dfrac { 1 }{ (1-x)^{ 1729 } } \right\} { x }^{ 6 }(1-x)^{ 6 } \, dx } =\dfrac { a}{ b }$

The equation above holds true for coprime positive integers $a$ and $b$. Find $a+b$.

**Bonus**: Generalize it.

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