\(\left(x-\dfrac{1}{9}\right)^3=\left(\dfrac{2}{3}\right)^6\)
\(\Rightarrow x^3-\left(\dfrac{1}{9}\right)^3=\left(\dfrac{2}{3}\right)^6\)
\(\Rightarrow x^3=\left(\dfrac{2}{3}\right)^6-\left(\dfrac{1}{9}\right)^3\)
\(x^3=\left(\dfrac{2^2}{3^2}\right)^3-\left(\dfrac{1}{9}\right)^3\)
\(x^3=\left(\dfrac{4}{9}\right)^3-\left(\dfrac{1}{9}\right)^3\)
\(x^3=\dfrac{7}{81}\)
\(\Rightarrow x=\sqrt[3]{\dfrac{7}{81}}\)