If
$$
\beta=\lim _{x \rightarrow 0} \frac{e^{r^3}-\left(1-x^{\frac{2}{3}}\right)^{\frac{1}{3}}\left((1-x)^2-1\right) \sin x}{x \sin ^2 x}
$$
then the value of $6 \beta$ is $\_\_\_\_$ .
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