We improve upon the cosmological constraints derived from the abundance and weak-lensing data of redMaPPer clusters detected in the Sloan Digital Sky Survey (SDSS). Specifically, we derive gas mass data using Chandra X-ray follow-up of a complete sample of the 30 richest SDSS redMaPPer clusters with $zin[0.1,0.3]$, and use these additional data to improve upon the original analysis by Costanzi et al. (2019b). We simultaneously fit for the parameters of the richness-mass relation, the cluster gas mass-mass relation, and cosmology. By including our X-ray cluster sample in the SDSS cluster cosmology analysis, we measure $Omega_{rm m} = 0.25 pm 0.04$ and $sigma_8 = 0.85^{+0.06}_{-0.08}$. These constraints represent a 25.5% and 29.8% reduction in the size of the 68% confidence intervals of $Omega_{rm m}$ and $sigma_8$ respectively, relative to the constraints published in Costanzi et al. (2019b). Our cosmological constraints are in agreement with early universe results from Planck. As a byproduct of our analysis, we also perform an independent calibration of the amplitude of the $langle M_{rm gas}^{rm true}|M_{rm 500c}rangle$ scaling relation. Our calibration is consistent with and of comparable precision to that of Mantz et al. (2016b).
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