Từ \(x=\frac{1}{3}\left(1+\sqrt[3]{\frac{12+\sqrt{135}}{3}}+\sqrt[3]{\frac{12-\sqrt{135}}{3}}\right)\)
\(\Rightarrow3x-1=\left(\sqrt[3]{\frac{12+\sqrt{135}}{3}}+\sqrt[3]{\frac{12-\sqrt{135}}{3}}\right)\)
\(\Leftrightarrow\left(3x-1\right)^3=\left(\sqrt[3]{\frac{12+\sqrt{135}}{3}}+\sqrt[3]{\frac{12-\sqrt{135}}{3}}\right)^3\)
\(\Rightarrow\left(3x-1\right)^3=8+3\left(3x+1\right)\)
\(\Leftrightarrow9x^3-9x^2-2=0\)
\(\Rightarrow M=-1\)