\(\left(\dfrac{1}{5}x+\dfrac{3}{7}\right)^3=\dfrac{-1}{8}\)
\(\Leftrightarrow\left(\dfrac{1}{5}x+\dfrac{3}{7}\right)^3=\left(\dfrac{-1}{2}\right)^3\)
\(\Rightarrow\dfrac{1}{5}x+\dfrac{3}{7}=\dfrac{-1}{2}\)
\(\Rightarrow\dfrac{1}{5}x=\dfrac{-13}{14}\)
\(\Rightarrow x=\dfrac{-65}{14}\)