Application Of Derivatives

Let $x=-1$ and $x=2$ be the critical points of the function $f(x)=x^3+a x^2+b \log _{\mathrm{e}}|x|+1, x \neq 0$.
Let $m$ and M respectively be the absolute minimum and the absolute maximum values of $f$ in the interval $\left[-2,-\frac{1}{2}\right]$. Then $|\mathrm{M}+m|$ is equal to
$\left(\right.$ Take $\left.\log _{\mathrm{e}} 2=0.7\right):$