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Algebra Level 4

Let \(r_{1}, r_{2}, ..., r_{2014}\) be the roots, not all necessarily distinct, of the polynomial \(x^{2014} + x^{20} + x^{14} + 2014.\) The polynomial with roots

\[\frac{r_{2}+r_{3}+\cdots+r_{2014}-r_{1}}{r_{2}^{2}+r_{3}^{2}+\cdots+r_{2014}^{2}-r_{1}^{2}}, \frac{r_{1}+r_{3}+\cdots+r_{2014}-r_{2}}{r_{1}^{2}+r_{3}^{2}+\cdots+r_{2014}^{2}-r_{2}^{2}}, \cdots, \frac{r_{1}+r_{2}+\cdots+r_{2013}-r_{2014}}{r_{1}^{2}+r_{2}^{2}+\cdots+r_{2013}^{2}-r_{2014}^{2}}\]

has the form \(ax^{b} + x^{c} + x^{d} + e\), for some positive integers \(a, b, c, d,\) and \(e\). Find \(a+b+c+d+e.\)

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