We present the first highly resolved measurements of the plasmon spectrum in an ultrafast heated solid. Multi-keV x-ray photons from the Linac Coherent Light Source have been focused to one micrometer diameter focal spots producing solid density aluminum plasmas with a known electron density of $n_{e} =1.8 x 10^{23} cm^{-3}$. Detailed balance is observed through the intensity ratio of up- and down-shifted plasmons in x-ray forward scattering spectra measuring the electron temperature. The plasmon damping is treated by electron-ion collision models beyond the Born approximation to determine the electrical conductivity of warm dense aluminum.