With the advent of 6G networks, efficient load balancing in indoor heterogeneous networks has become critical to address the proliferation of connected devices and the demand for high data rates. This paper introduces a Monte Carlo tree search (MCTS)-based load balancing algorithm for 6G indoor heterogeneous networks, exemplified by hybrid visible light communication (VLC) and radio frequency (RF) systems. By dynamically predicting future network states, the proposed algorithm optimally distributes traffic, improving overall network performance. Simulation results show that the proposed MCTS-based method increases average user throughput by 13-60%, reduces handover rates by around 50%, and lowers latency by 15-50% as compared to benchmark methods while maintaining balanced computational complexity. These findings highlight the potential of MCTS as an effective and scalable solution for load balancing in complex 6G network environments.