Let $\alpha$ be a solution of $x^2+x+1=0$, and for some $a$ and $b$ in $\mathbb{R},\left[\begin{array}{lll}4 & a & b\end{array}\right]\left[\begin{array}{ccc}1 & 16 & 13 \\ -1 & -1 & 2 \\ -2 & -14 & -8\end{array}\right]=\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]$. If $\frac{4}{\alpha^4}+\frac{m}{\alpha^a}+\frac{n}{\alpha^b}=3$, then $m+n$ is equal to