\(\frac{11}{12}-\left(\frac{2}{5}+x\right)=\frac{2}{3}.\left(6x+1\right)\)
\(\Rightarrow\frac{11}{12}-\frac{2}{5}-x=\frac{2}{3}.6x+\frac{2}{3}\)
\(\Rightarrow\frac{55-24}{60}-x=4x+\frac{2}{3}\)
\(\Rightarrow\frac{31}{60}-x=4x+\frac{2}{3}\)
\(\Rightarrow\frac{31}{60}-\frac{2}{3}=4x+x=5x\)
\(\Rightarrow5x=-\frac{11}{60}\)
\(\Rightarrow x=\frac{-11}{300}\)