Large language models (LLMs) have recently demonstrated strong potential for sequential recommendation. However, current LLM-based approaches face critical limitations in modeling users' long-term and diverse interests. First, due to inference latency and feature fetching bandwidth constraints, existing methods typically truncate user behavior sequences to include only the most recent interactions, resulting in the loss of valuable long-range preference signals. Second, most current methods rely on next-item prediction with a single predicted embedding, overlooking the multifaceted nature of user interests and limiting recommendation diversity. To address these challenges, we propose HyMiRec, a hybrid multi-interest sequential recommendation framework, which leverages a lightweight recommender to extracts coarse interest embeddings from long user sequences and an LLM-based recommender to captures refined interest embeddings. To alleviate the overhead of fetching features, we introduce a residual codebook based on cosine similarity, enabling efficient compression and reuse of user history embeddings. To model the diverse preferences of users, we design a disentangled multi-interest learning module, which leverages multiple interest queries to learn disentangles multiple interest signals adaptively, allowing the model to capture different facets of user intent. Extensive experiments are conducted on both benchmark datasets and a collected industrial dataset, demonstrating our effectiveness over existing state-of-the-art methods. Furthermore, online A/B testing shows that HyMiRec brings consistent improvements in real-world recommendation systems. Code is available at https://github.com/FireRedTeam/FireRedSeqRec.