In this work, we introduce a framework for speech summarization that leverages the processing and reasoning capabilities of large language models (LLMs). We propose an end-to-end system that combines an instruction-tuned LLM with an audio encoder that converts speech into token representations that the LLM can interpret. Using a dataset with paired speech-text data, the overall system is trained to generate consistent responses to prompts with the same semantic information regardless of the input modality. The resulting framework allows the LLM to process speech inputs in the same way as text, enabling speech summarization by simply prompting the LLM. Unlike prior approaches, our method is able to summarize spoken content from any arbitrary domain, and it can produce summaries in different styles by varying the LLM prompting strategy. Experiments demonstrate that our approach outperforms a cascade baseline of speech recognition followed by LLM text processing.