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(-1) is presented. No significant excess over the expected standard model prediction is observed. In this data set, 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(-1) diphoton analysis, the RS-graviton lower-mass limit for the coupling k/M¯(Pl)=0.1 is 1058 GeV/c(2), making it the strongest limit to date.