First off: LDL cholesterol (aka the “bad cholesterol”) isn’t entirely useless. When the liver needs to make bile (which is needed for fat digestion), it takes the cholesterol from LDL.
So fibre, is indigestible for the most part. It also prevents the body from reabsorbing bile after it is released. Fibre mixes with bile and is excreted in feces. So what happens when the body is low on bile? Well thats when LDL-cholesterol is pulled from the blood and into the liver to make more bile.
Research shows that “soluble” fibre is most effective at lowering cholesterol. Look for foods such as oats, peas, citrus fruits, etc.
So there you go, hope that was informative.