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