Recent efforts have extended textual LLMs to the speech domain. Yet, a key challenge remains, which is balancing speech understanding and generation while avoiding catastrophic forgetting when integrating acoustically rich codec-based representations into models originally trained on text. In this work, we propose a novel approach that leverages continual pre-training (CPT) on a pre-trained textual LLM to create a codec-based speech language model. This strategy mitigates the modality gap between text and speech, preserving the linguistic reasoning of the original model while enabling high-fidelity speech synthesis. We validate our approach with extensive experiments across multiple tasks, including automatic speech recognition, text-to-speech, speech-to-text translation, and speech-to-speech translation (S2ST), demonstrating that our model achieves superior TTS performance and, notably, the first end-to-end S2ST system based on neural codecs.