1. Let the real number $a$ satisfy $a<9 a^{3}-11 a<|a|$. Then the range of values for $a$ is $\qquad$ .
$$
\text { -1. } a \in\left(-\frac{2 \sqrt{3}}{3},-\frac{\sqrt{10}}{3}\right) \text {. }
$$

From $a<|a| \Rightarrow a<0$.
Then from the original inequality we get
$$
-1<9 a^{2}-11<1 \Rightarrow a^{2} \in\left(\frac{10}{9}, \frac{4}{3}\right) \text {. }
$$

Since $a<0$, thus $a \in\left(-\frac{2 \sqrt{3}}{3},-\frac{\sqrt{10}}{3}\right)$.