The ultra-diffuse galaxy in the NGC 5846 group (NGC 5846_UDG1) was shown to have a large number of globular cluster (GC) candidates from deep imaging as part of the VEGAS survey. Recently, Muller et al. published a velocity dispersion, based on a dozen of its GCs. Within their quoted uncertainties, the resulting dynamical mass allowed for either a dark matter free or a dark matter dominated galaxy. Here we present spectra from KCWI which reconfirms membership of the NGC 5846 group and reveals a stellar velocity dispersion for UDG1 of $sigma_{GC}$ = 17 $pm$ 2 km/s. Our dynamical mass, with a reduced uncertainty, indicates a very high contribution of dark matter within the effective radius. We also derive an enclosed mass from the locations and motions of the GCs using the Tracer Mass Estimator, finding a similar mass inferred from our stellar velocity dispersion. We find no evidence that the galaxy is rotating and is thus likely pressure-supported. The number of confirmed GCs, and the total number inferred for the system ($sim$45), suggest a total halo mass of $sim2 times 10^{11}$ M$_{odot}$. A cored mass profile is favoured when compared to our dynamical mass. Given its stellar mass of 1.1$times$10$^{8}$ M$_{odot}$, NGC 5846_UDG1 appears to be an ultra-diffuse galaxy with a dwarf-like stellar mass and an overly massive halo.