The solubility product of a sparingly soluble salt \( A_2X_3 \) is \( 1.1 \times 10^{-23} \). If specific conductance of the solution is \( 3 \times 10^{-5} \, \text{S m}^{-1} \), the limiting molar conductivity of the solution is \( x \times 10^{-3} \, \text{S m}^2 \text{ mol}^{-1} \). The value of \( x \) is ______.
