\(2x+\dfrac{1}{2}+4x+\dfrac{1}{6}+6x+\dfrac{1}{6}=12\dfrac{11}{12}\Leftrightarrow\)\(2x+\dfrac{1}{2}+4x+\dfrac{1}{6}+6x+\dfrac{1}{6}=\dfrac{155}{12}\)\(\Leftrightarrow24x+6+48x+2+72x+2=155\)\(\Leftrightarrow24x+48x+72x=155-6-2-2\)\(\Leftrightarrow144x=145\)\(\Leftrightarrow x=\dfrac{145}{144}\)