Communication by jointly precoded transmission from many distributed access points (APs), called cell-free massive multiple-input multiple-output (CF mMIMO), is a promising concept for beyond 5G systems. One of the challenging aspects of CF mMIMO is an efficient management of the radio resources. We propose both reinforcement learning (RL)-based and heuristic precoding aware radio resource scheduling (RRS) algorithms aiming at maximizing sum spectral efficiency (SE). The proposed algorithms allocate resources for Maximum Ratio Transmission (MRT), Zero-Forcing (ZF) and Regularised Zero-Forcing (RZF) precoders. For the resource allocation, both the set of serving APs and the Physical Resource Blocks are considered. In high noise scenarios, the proposed RL-based RRS algorithm combined with the MRT precoder shows 2.4 times higher sum SE than the standard Round Robin scheduler. Moreover, we demonstrate that the proposed heuristic algorithms offer similar sum SE while significantly reducing the complexity compared to the RL-based solution. We also show that the RZF precoding, which is superior to the ZF precoding in noisy environments, results overall in more transmitted power. Therefore, assuming the same radio resource schedule and precoding strategy in the neighbouring cells, it will result in more inter-cell interference and an overall reduced performance.