If $\lim _{\mathrm{t} \rightarrow 0}\left(\int_{0}^{1}(3 x+5)^{\mathrm{t}} \mathrm{d} x\right)^{\frac{1}{\mathrm{t}}}=\frac{\alpha}{5 \mathrm{e}}\left(\frac{8}{5}\right)^{\frac{2}{3}}$, then $\alpha$ is equal to $\_\_\_\_$ .
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