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 \(m+n+r\).

(第十八届AIME2 2000 第13题)