We propose a novel framework for electrolaryngeal speech intelligibility enhancement through the use of robust linguistic encoders. Pretraining and fine-tuning approaches have proven to work well in this task, but in most cases, various mismatches, such as the speech type mismatch (electrolaryngeal vs. typical) or a speaker mismatch between the datasets used in each stage, can deteriorate the conversion performance of this framework. To resolve this issue, we propose a linguistic encoder robust enough to project both EL and typical speech in the same latent space, while still being able to extract accurate linguistic information, creating a unified representation to reduce the speech type mismatch. Furthermore, we introduce HuBERT output features to the proposed framework for reducing the speaker mismatch, making it possible to effectively use a large-scale parallel dataset during pretraining. We show that compared to the conventional framework using mel-spectrogram input and output features, using the proposed framework enables the model to synthesize more intelligible and naturally sounding speech, as shown by a significant 16% improvement in character error rate and 0.83 improvement in naturalness score.