Cubes Are King

Algebra Level 3

\[\dfrac{{1}^3+{2}^3+\cdots+{2016}^3}{({1}+{2}+\cdots+{2016})({1}^2+{2}^2+\cdots+{2016}^2)}\]

If the value of above expression can be expressed in the form of \(\dfrac{a}{b},\) where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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