If the domain of the function $\log _{5}\left(18 x-x^{2}-77\right)$ is ( $\alpha, \beta$ ) and the domain of the function $\log _{(x-1)}\left(\frac{2 x^{2}+3 x-2}{x^{2}-3 x-4}\right)$ is $(\gamma, \delta)$, then $\alpha^{2}+\beta^{2}+\gamma^{2}$ is equal to :
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