  Cosmic voids identified in the spatial distribution of galaxies provide
complementary information to two-point statistics. In particular, constraints
on the neutrino mass sum, $\sum m_\nu$, promise to benefit from the inclusion
of void statistics. We perform inference on the CMASS NGC sample of
SDSS-III/BOSS with the aim of constraining $\sum m_\nu$. We utilize the void
size function, the void galaxy cross power spectrum, and the galaxy auto power
spectrum. To extract constraints from these summary statistics we use a
simulation-based approach, specifically implicit likelihood inference. We
populate approximate gravity-only, particle neutrino cosmological simulations
with an expressive halo occupation distribution model. With a conservative
scale cut of kmax=0.15 h/Mpc and a Planck-inspired LCDM prior, we find upper
bounds on $\sum m_\nu$ of 0.43 and 0.35 eV from the galaxy auto power spectrum
and the full data vector, respectively (95% credible interval). We observe
hints that the void statistics may be most effective at constraining $\sum
m_\nu$ from below. We also substantiate the usual assumption that the void size
function is Poisson distributed.
