We present the results of a combined fit of the reactor antineutrino rates and the Daya Bay measurement of ${\ensuremath{\sigma}}_{f,235}$ and ${\ensuremath{\sigma}}_{f,239}$. The combined fit leads to a better determination of the two cross sections per fission: ${\ensuremath{\sigma}}_{f,235}=6.29\ifmmode\pm\else\textpm\fi{}0.08$ and ${\ensuremath{\sigma}}_{f,239}=4.24\ifmmode\pm\else\textpm\fi{}0.21$ in units of ${10}^{\ensuremath{-}43}\text{ }\text{ }{\mathrm{cm}}^{2}/\text{fission}$, with respective uncertainties of about 1.2% and 4.9%. Since the respective deviations from the theoretical cross sections per fission are $2.5\ensuremath{\sigma}$ and $0.7\ensuremath{\sigma}$, we conclude that, if the reactor antineutrino anomaly is not due to active-sterile neutrino oscillations, it is likely that it can be solved with a revaluation of the $^{235}\mathrm{U}$ reactor antineutrino flux. However, the $^{238}\mathrm{U}$, $^{239}\text{Pu}$, and $^{241}\mathrm{Pu}$ fluxes, which have larger uncertainties, could also be significantly different from the theoretical predictions.