Let $x=\dfrac{m}{n}$ ($m,n$ are co-prime natural numbers) be a solution of the equation $\cos\!\left(2\sin^{-1}x\right)=\dfrac{1}{9}$ and let $\alpha,\beta\ (\alpha>\beta)$ be the roots of the equation $m x^{2}-n x-m+n=0$. Then the point $(\alpha,\beta)$ lies on the line