Nested Summation

Algebra Level 3

n=120161+2+3++n13+23+33++n3 \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 AB\frac{A}{B}, where AA and BB are coprime positive integers, find A+B.A + B.

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