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.
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