Cleaning a sponge painted wall?

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I moved into a house that has a gorgeous painted wall that has a sponge painted texture.
All I can do to clean it is vacuum with a brush attachment.
I try washing it with water but it shreds all cleaning rags and towels and leaves "lint-like" residue from the cloths.
It's not THAT textured but washing seems impossible.. and now is "linty" too.
Any "sponge-paint" experts out there with solutions?

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