\(\left(5x-1\right)^6=729=3^6=\left(-3\right)^6\)
\(\Rightarrow\left[{}\begin{matrix}5x-1=3\\5x-1=-3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}5x=4\\5x=-2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{4}{5}\\x=-\dfrac{2}{5}\end{matrix}\right.\)