The solubility product of a sparingly soluble salt A₂X₃ is 1.1 $\times$ 10^$-$23. If specific conductance of the solution is 3 $\times$ 10^$-$5 S m^$-$1, the limiting molar conductivity of the solution is $x \,\times$ 10^$-$3 S m² mol^$-$1. The value of x is ___________.