When All Else Fails, We Don't

Algebra Level 5

\[\large 2000x^{6} + 100x^{5} + 10x^{3} + x - 2 = 0\]

One of the roots of the equation above is of the form \(\dfrac{m + \sqrt{n}}{r}\), where \(m\) is a non-zero integer, \(r\) and \(n\) are relatively coprime positive integers.

Find the value of \(m + n + r\).

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