Is it even possible to actually cure them? I have them as well. Whenever I'm using an anitbiotic like clindamycin gel or even benzaclin, I notice a difference. Recently I've been experimenting with chemical peels and toners and have found lactic peels and mandelic toner to work great. I bought them from MUAC and like them. You can also find other brands online.
No amount of cleansing will stop sebaceous filaments from forming, nor will extraction via pore strips or squeezing keep them from coming back within days. Treating healthy skin with aggressive products designed to combat acne won't remove those filaments; in fact, overly aggressive treatments could cause more problems than they solve. Focus on reducing the visibility of sebaceous filaments rather than their removal.