Nested Summation

Algebra Level 3

\[\large \sum _{ n=1 }^{ 2016 }{ \dfrac { 1+2+3+\dots +n }{ { 1 }^{ 3 }+{ 2 }^{ 3 }+{ 3 }^{ 3 }+\dots +{ n }^{ 3 } } } \]

If the value of this sum is \(\dfrac{A}{B}\), where \(A\) and \(B\) are coprime positive integers, find \(A + B.\)

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