About 80% of the cholesterol in your body is created by your liver, and if you eat less cholesterol your liver will make more and vice versa - so diet only has a relatively small effect.
Some people absorb more cholesterol than others and others absorb less cholesterol than others — so there are genetic factors too.
The foods made to lower cholesterol do so by including stanols which compete with cholesterol for absorption.
6.5 isn’t high - mine was over 11 at one point but not had it checked for 3 years.
In the 70s they talked of high cholesterol and low cholesterol.
Then medicine advanced and in the 90s doctors talked about good cholesterol and bad cholesterol.
Now medicine has advanced further and consultants should know that there is a big difference between large cholesterol particles and small cholesterol particles - so big LDL can be “good” and small LDL is thought to be “less good” as it’s more likely to get under the endothelium.
As someone who had a heart attack 3 years ago, I must comment that my consultant cardiologist has no problems with me eating a keto diet with plenty of eggs.
Eating more leafy greens is never going to be bad advice, same for eating some good quality oily fish and less processed food. If you want to lose weight stopping eating all grains is what worked for me.