Another form presents geometric sequence

Algebra Level 3

\[\large \sum_{k=1}^{2016}x^k=\frac{x-2016}{1-x}\]

If the real root of the equation above is of the form \(\large \sqrt[a]{b}\), where \(a\) and \(b\) are positive integers with \(a\) minimized, find \(a+b\).

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