If domain of the function \({\log }_{e}\left(\frac{6{x}^{2}+5x+1}{2x-1}\right)+{\cos }^{-1}\left(\frac{2{x}^{2}-3x+4}{3x…

If domain of the function
\({\log }_{e}\left(\frac{6{x}^{2}+5x+1}{2x-1}\right)+{\cos }^{-1}\left(\frac{2{x}^{2}-3x+4}{3x-5}\right)\text{ is }(\alpha ,\beta )\cup (\gamma ,\delta ]\text{, }\)
then \(18\left({\alpha }^{2}+{\beta }^{2}+{\gamma }^{2}+{\delta }^{2}\right)\) is equal to _____ .

[JEE Main 2023, 8 Apr (Shift 2)]