If the domain of the function \(f\left(x\right)={\log }_{e}\left(4{x}^{2}+11x+6\right)+{\sin }^{-1}\left(4x+3\right)+{\c…

If the domain of the function \(f\left(x\right)={\log }_{e}\left(4{x}^{2}+11x+6\right)+{\sin }^{-1}\left(4x+3\right)+{\cos }^{-1}\left(\frac{10x+6}{3}\right)\) is \((\alpha ,\beta ]\), then \(36|\alpha +\beta |\) is equal to:

[JEE Main 2023, 15 Apr (Shift 1)]