Rate splitting multiple access (RSMA) provides a flexible transmission framework that can be applied in mobile edge computing (MEC) systems. However, the research work on RSMA-assisted MEC systems is still at the infancy and many design issues remain unsolved, such as the MEC server and channel allocation problem in general multi-server and multi-channel scenarios as well as the user fairness issues. In this regard, we study an RSMA-assisted MEC system with multiple MEC servers, channels and devices, and consider the fairness among devices. A max-min fairness computation offloading problem to maximize the minimum computation offloading rate is investigated. Since the problem is difficult to solve optimally, we develop an efficient algorithm to obtain a suboptimal solution. Particularly, the time allocation and the computing frequency allocation are derived as closed-form functions of the transmit power allocation and the successive interference cancellation (SIC) decoding order, while the transmit power allocation and the SIC decoding order are jointly optimized via the alternating optimization method, the bisection search method and the successive convex approximation method. For the channel and MEC server allocation problem, we transform it into a hypergraph matching problem and solve it by matching theory. Simulation results demonstrate that the proposed RSMA-assisted MEC system outperforms current MEC systems under various system setups.