\(\left(4x-1\right)^3=\frac{-1}{27}\)
\(\Rightarrow\left(4x-1\right)^3=\left(\frac{-1}{3}\right)^3\)
\(\Rightarrow4x-1=\frac{-1}{3}\)
\(\Rightarrow4x=\frac{-1}{3}+1\)
\(\Rightarrow4x=\frac{2}{3}\)
\(\Rightarrow x=\frac{2}{3}:4\)
\(\Rightarrow x=\frac{1}{6}\)