The aggregated visible light communication (VLC) and radio frequency (RF) system, which can be regarded as a heterogeneous multiple-input multiple-output system, has been studied to operate with novel multiple access technologies for effectively expanding spectrum resources. In this paper, we propose a novel cooperative rate splitting multiple access (RSMA)-based aggregated VLC/RF system that forwards part of common stream via device-to-device (D2D) RF sidelinks to tackle the problem of fairness among users. Meanwhile, with the objective of maximizing the minimum achievable rate, we jointly optimize the precoder, the rate allocation of the common stream, and the transmission power allocation of RF sidelink communication under the constraint of limited total system power. Since the optimization problem is non-convex, we propose an algorithm based on semidefinite relaxation (SDR) and successive convex approximation (SCA) methods to solve it by adopting the slack variables and linear approximation. Numerical results show that the proposed scheme significantly outperforms other baseline schemes in terms of user fairness, i.e., the minimum achievable rate, in different scenarios.