Some people can get benefit out of a quick cleaning - like 15 minutes in vodka or grain alcohol (some use rubbing alcohol but that's a poison so I don't). Make sure it's all wet inside and submerged and leave for 15 minutes. Then scoop some alcohol through it to rinse, then shake it out into the sink, pat the outside dry and blow dry or blow through it until it's dry inside, especially the bridge area.
There is also a way to clean with pouring boiling water but that would take longer to dry.
And BTW - your cart stuffing might be gunky too. I can only get 4-5 days of good taste out of the same white cart stuffing then I switch it to blue foam. And if I fool around too much mixing in the cart, or use thick or oil-flavoring juices, even my blue stuffing can get a bit icky so if that happens I hold the stuffing under running water, pat dry with paper towels. I also rinse the cart and shake dry. This past weekend I needed both a clean atty and a cart/foam cleaning.
It is possible to clean some white stuffings (maybe with alcohol instead of running water) but I can never get them back right. You can also buy polyfill stuffing from the craft store and use that as stuffing but I think blue foam is better. For 510 you can get precut blue foam at strictlyejuice.com (says they are for 901 too but some 901 carts are a different shape I don't think the precuts would work in). or you can cut your own from Marineland Rite-SIze U Foam Sleeve from the aquarium dept of Petsmart.