Consider a binary mixture of components $A$ and $B$ at temperature $T$ and pressure $P$. Let $\bar{V}_{A}$ and $\bar{V}_{B}$ be the partial molar volumes of $A$ and $B$, respectively. At a certain mole fraction of $A, x_{A}$
\[
\left(\frac{\partial \bar{V}_{A}}{\partial x_{A}}\right)_{T, P}=22 \mathrm{~cm}^{3} \mathrm{~mol}^{-1} \text { and }\left(\frac{\partial \bar{V}_{B}}{\partial x_{A}}\right)_{T, P}=-18 \mathrm{~cm}^{3} \mathrm{~mol}^{-1}
\]
The value of $x_{A}$, rounded off to $2$ decimal places, is $\_\_\_\_\_\_\_\_\_$.