Oil pulling is probably the only way that works.

The reason is because not everything in the mouth is water-soluble. Lipase in our saliva can mix with oil to form a bacterial cell wall-degrading enzyme.

Also, the cadmium in our body can be excreted in sweat, urine and/or saliva. According to some biochemistry literature, saliva is apparently the most efficient medium for excreting cadmium.

[link to www.sciencedirect.com]