Using Vieta's Formula?

Algebra Level 4

\[\large 2016x^{3}+2015x^{2}+2014x+2016=0\]

Let \(\alpha\) , \(\beta\) and \(\gamma\) be the roots of the equation above .

Find the value of :

\[\dfrac{2016(\alpha^3+\beta^3+\gamma^3)+2015(\alpha^2+\beta^2+\gamma^2)+2014(\alpha+\beta+\gamma)}{2016(\alpha^3-\beta^3-\gamma^3)+2015(\alpha^2-\beta^2-\gamma^2)+2014(\alpha-\beta-\gamma)}\]

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