If $\lim _{x\to 2}\frac{\sin \left({x}^{3}-5{x}^{2}+ax+b\right)}{(\sqrt{x-1}-1){\log }_{e}(x-1)}=m$, then $a+b+m$ is equal to: [JEE Main 2026, 2 Apr (Shift 1)]

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If \(\lim _{x\to 2}\frac{\sin \left({x}^{3}-5{x}^{2}+ax+b\right)}{(\sqrt{x-1}-1){\log }_{e}(x-1)}=m\), then \(a+b+m\) is…

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