Group them in a nice way

Algebra Level 5

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

The equation above has two real roots one of which is \(\dfrac{m+\sqrt{n}}{r}\) for integers \(m,n,r\) with \(n\) square free and \(r\) positive.

Find \(m+n+r\).

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