Empty the tank and rinse out. Take a wire coat hanger or a 1/8" welding rod and flatten one end ( hammer and solid surface to pound on). Bend the rod into a 90 degree bend about 1" from the flattened end. With the valve open use the flattened end to clean out the slot that the valve gate moves and seats in. While there lube the slot with a generous amount of water proof grease. The green lube that boat shops use on outdrives and outboard motors when changing props works real well and stays put. I do not remember the name of it tho.
I bet your local boat shop will be familiar with it tho. I have an old tube from years past and it works super and lasts forever.
This suggestion also applies to the grey water valve. While there , might as well do both. By the way ! some rv accessory stores sell a tool for this Made somewhat like what I have described.