More fun in 2016 part 2

Calculus Level pending

\[ \displaystyle\lim _{ n\rightarrow \infty }{ \displaystyle\int _{ 0 }^{ 1 }{ \cdots \displaystyle\int _{ 0 }^{ 1 }{ \sqrt [ n ]{ \displaystyle \left( \prod _{ k=1 }^{ n }{ { x }_{ k } } \right )^{ 2016 }}d{ x }_{ 1 }d{ x }_{ 2 }\cdots d{ x }_{ { n } } } } }=\dfrac { a }{ { e }^{ b } } \]

The equation above holds true for positive integers \(a\) and \(b\). Find \(a+b\).

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