Change toothpaste. Others have experienced a slimy or stringy substance in their mouths after brushing. It seems more common after using toothpastes with whitening agents. Some get it after using a mouthwash following brushing. I'd recommend trying a toothpaste designed to be more gentle. Brush without toothpaste for 3 days, then restart with a gentler or "natural" toothpaste. See your dentist if not resolving.
Toothpaste reaction. Possbile that your toothpaste may be irritating the mouth tissues . Some toothpaste ingredients can react negatively to the mouth. Switch to non irritating toothpaste.
Toothpaste. If the white slime only appears after brushing your teeth and you are brushing with toothpaste, the white slime could be a combination of residual toothpaste mixed with your saliva.