If the range of \(x\) that satisfies
\[{5}^{\log_{9}x} \cdot {x}^{\log_{9}{5}}-3({5}^{\log_{9}x}+{x}^{\log_{9}{5}})+5 < 0\]
is \(\alpha < x < \beta,\) what is the value of \(\alpha+\beta?\)

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If the range of \(x\) that satisfies the logarithmic inequality
\[(\log_{5}x)^2-\log_{5}125x^{2} \leq 0\]
is \(\alpha \leq x \leq \beta,\) what is the value of \(\alpha\beta?\)

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