Partial fraction challenge (2)

Algebra Level 4

\[ S =\frac{1}{1^{4}+1^{2}+1}+\frac{2}{2^{4}+2^{2}+1}+\frac{3}{3^{4}+3^{2}+1}+\dots+\frac{2016}{2016^{4}+2016^{2}+1}\]

If the sum above \(S = \dfrac{2017p}{2017q+1}\), where \(p\) and \(q\) are positive integers, find \(p+q\).

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