2000 AIME II Problem 13

The equation 2000x^6+100x^5+10x^3+x-2=0 has exactly two real roots, one of which is \frac{m+\sqrt{n}}r, where m, n and r are integers, m and r are relatively prime, and r>0. Find m+n+r.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.