Abstract: We consider the ratio of the spectra measured in the DANSS neutrino experiment at 12.7 and 10.7 m from a nuclear reactor. These data give a new model-independent indication in favor of short-baseline (nu) over bar (e) oscillations which reinforce the model-independent indication found in the late 2016 in the NEOS experiment. The combined analysis of the NEOS and DANSS spectral ratios in the framework of 3+1 active-sterile neutrino mixing favor short-baseline (nu) over bar (e) oscillations with a statistical significance of 3.7 sigma. The two mixing parameters sin(2)2 nu ee and Delta m(41)(2) are constrained at 2 sigma a narrow-Delta m(41)(2) island at Delta m(41)(2) similar or equal to 1.3 eV(2), with sin(2)2 nu(ee)= 0.049 +/- 0.023(2 sigma). We discuss the implications of the model-independent NEOS+DANSS analysis for the reactor and Gallium anomalies. The NEOS+DANSS model-independent determination of short-baseline (nu) over bar (e) oscillations allows us to analyze the reactor rates without assumptions on the values of the main reactor antineutrino fluxes and the data of the Gallium source experiments with free detector efficiencies. The corrections to the reactor neutrino fluxes and the Gallium detector efficiencies are obtained from the fit of the data. In particular, we confirm the indication in favor of the need for a recalculation of the (235)Ureactor antineutrino flux found in previous studies assuming the absence of neutrino oscillations.