A search for new dielectron-mass resonances using data recorded by the CDF II detector and corresponding to an integrated luminosity of $5.7\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ 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 ($960\text{ }\text{ }\mathrm{GeV}/{c}^{2}$) was recorded. The results are interpreted in the Randall-Sundrum (RS) model. Combined with the $5.4\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ diphoton analysis, the RS-graviton lower-mass limit for the coupling $k/{\overline{M}}_{\mathrm{Pl}}=0.1$ is $1058\text{ }\text{ }\mathrm{GeV}/{c}^{2}$, making it the strongest limit to date.