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

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

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