Yes, exercise does not affect it. If it's a small polyp, or it doesn't affect the sound, and the sound is not hoarse, then it will be fine after a rest. However, polyps generally do not fully recover. Liu Huan also had vocal cord surgery, but he had it abroad in his early years. Although this kind of operation is small, it is very difficult to do it well. Most of his voice will change. Even if the operation is done well, it depends on the postoperative recovery.
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