Let $\alpha, \beta(\alpha \neq \beta)$ be the values of $m$, for which the equations $x+y+z=1 ; x+2 y+4 z=m$ and $x+4 y+10 z=m^{2}$ have infinitely many solutions. Then the value of $\displaystyle\sum_{n=1}^{10}\left(n^{\alpha}+n^{\beta}\right)$ is equal to :
