  Using 5.9~pb$^{-1}$ of $e^+e^-$ annihilation data collected at center-of-mass
energies from 3.640 to 3.701 GeV with the BESIII detector at the BEPCII
Collider, we measure the observed cross sections of $e^+e^-\rightarrow
K_{S}^{0} X$ (where $X= \text{anything}$). From a fit to these observed cross
sections with the sum of continuum and $\psi(3686)$ and $J/\psi$ Breit-Wigner
functions and considering initial state radiation and the BEPCII beam energy
spread, we obtain for the first time the product of $\psi(3686)$ leptonic width
and inclusive decay branching fraction $\Gamma^{ee}_{\psi(3686)}\mathcal
B(\psi(3686)\rightarrow K_{S}^{0} X) = (373.8 \pm 6.7 \pm 20.0)$ eV, and
assuming $\Gamma^{ee}_{\psi(3686)}$ is $(2.33 \pm 0.04)$ keV from PDG value, we
measure $\mathcal B(\psi(3686)\rightarrow K_{S}^{0} X) = (16.04 \pm 0.29 \pm
0.90)\%$, where the first uncertainty is statistical and the second is
systematic.
