Let \(x=-1\) and \(x=2\) be the critical points of the function \(\mathrm{f}(\mathrm{x})={\mathrm{x}}^{3}+{\mathrm{ax}}^…

Let \(x=-1\) and \(x=2\) be the critical points of the function \(\mathrm{f}(\mathrm{x})={\mathrm{x}}^{3}+{\mathrm{ax}}^{2}+{\mathrm{blog}}_{\mathrm{e}}|\mathrm{x}|+1,\mathrm{x}\neq 0\). 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 ( Take \({\log }_{\mathrm{e}}2=0.7\)):

[JEE Main 2025, 7 Apr (Shift 1)]