309*. Solve the equation:

$$
x^{3}+x^{2}+x=-\frac{1}{3}
$$
$\triangle$ Transform the equation:

$$
\begin{gathered}
3 x^{3}+3 x^{2}+3 x+1=0 \\
\left(x^{3}+3 x^{2}+3 x+1\right)=-2 x^{3} \\
(x+1)^{3}=-2 x^{3}
\end{gathered}
$$

Then

$$
x+1=-x \sqrt[3]{2}, \quad x=-\frac{1}{1+\sqrt[3]{2}}
$$

Answer: $-\frac{1}{1+\sqrt[3]{2}}$.