Let $x = - 1$ and $x = 2$ be the critical points of the function $f(x) = {x^3} + a{x^2} + b{\log _{\rm{e}}}|x| + 1,x \ne 0$. 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 $|{\bf{M}} + m|$ is equal to_____. (Take $\left. {{{\log }_e}2 = 0.7} \right)$ :