Low Earth Orbit (LEO) satellite communication (SatCom) has drawn particular attention recently due to its high data rate services and low round-trip latency. It has low launching and manufacturing costs than Medium Earth Orbit (MEO) and Geostationary Earth Orbit (GEO) satellites. Moreover, LEO SatCom has the potential to provide global coverage with a high-speed data rate and low transmission latency. However, the spectrum scarcity might be one of the challenges in the growth of LEO satellites, impacting severe restrictions on developing ground-space integrated networks. To address this issue, cognitive radio and rate splitting multiple access (RSMA) are the two emerging technologies for high spectral efficiency and massive connectivity. This paper proposes a cognitive radio enabled LEO SatCom using RSMA radio access technique with the coexistence of GEO SatCom network. In particular, this work aims to maximize the sum rate of LEO SatCom by simultaneously optimizing the power budget over different beams, RSMA power allocation for users over each beam, and subcarrier user assignment while restricting the interference temperature to GEO SatCom. The problem of sum rate maximization is formulated as non-convex, where the global optimal solution is challenging to obtain. Thus, an efficient solution can be obtained in three steps: first we employ a successive convex approximation technique to reduce the complexity and make the problem more tractable. Second, for any given resource block user assignment, we adopt KarushKuhnTucker (KKT) conditions to calculate the transmit power over different beams and RSMA power allocation of users over each beam. Third, using the allocated power, we design an efficient algorithm based on the greedy approach for resource block user assignment. For comparison, we propose two suboptimal schemes with fixed power allocation over different beams and random resource block user assignment as the benchmark. Numerical results provided in this work are obtained based on the Monte Carlo simulations, which demonstrate the benefits of the proposed optimization scheme compared to the benchmark schemes.