A search for new dielectron mass resonances using data recorded by the CDF II detector and corresponding to an integrated luminosity of 5.7/fb is presented. No significant excess over the expected standard model prediction is observed. In this dataset, an event with the highest dielectron mass ever observed (960 GeV/c^2) was recorded. The results are interpreted in the Randall-Sundrum (RS) model. Combined with the 5.4/fb diphoton analysis, the RS-graviton lower mass limit for the coupling k/bar{M}_{Pl}=0.1 is 1058 GeV/c^2, making it the strongest limit to date.