When All Else Fails, We Don't

Algebra Level 5

2000x6+100x5+10x3+x2=0\large 2000x^{6} + 100x^{5} + 10x^{3} + x - 2 = 0

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

Find the value of m+n+rm + n + r.

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