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We present cross sections for the reaction e+e−→K0SK0L at center-of-mass energies ranging from 3.51 GeV to 4.95 GeV using data samples collected in the BESIII experiment, corresponding to a total integrated luminosity of 26.5 fb−1. The ratio of neutral-to-charged kaon form factors at large momentum transfers (12 GeV2<Q2<25 GeV2) is determined to be 0.21±0.01, which indicates a small but significant effect of flavor-SU(3) breaking in the kaon wave function, and consequently excludes the possibility that flavor-SU(3) breaking is the primary reason for the strong experimental violation of the pQCD prediction |F(π±)|/|F(K±)|=f2π/f2K, where F(π±) and F(K±) are the form factors, and fπ and fK are the decay constants of charged pions and kaons, respectively. We also observe a significant signal for the charmless decay ψ(3770)→K0SK0L for the first time. Within a 1σ contour of the likelihood value, the the branching fraction for ψ(3770)→K0SK0L is determined to be B=(2.63+1.40−1.59)×10−5, and the relative phase between the continuum and ψ(3770) amplitudes is ϕ=(−0.39+0.05−0.10)π. The branching fraction is in good agreement with the S- and D-wave charmonia mixing scheme proposed in the interpretation of the "ρπ puzzle" between J/ψ and ψ(3686) decays.