Cholesterol: How can you lower LDL and maintain OR raise HDL?

Everywhere I look online (e.g. Cleveland Clinic), it says about keeping LDL (Low Density Lipoproteins) to less than 100mg/dL and where possible raise HDL (High Density Lipoproteins) to 50mg/dL or higher and reaching this is considered to be good. HDL of 60 or more is considered to be optimum and a protection against heart disease.

Now, What natural supplements exist to lower LDL cholesterol and raise HDL cholesterol? asks for natural remedies, but I am asking what dietary changes will help lower LDL and at the same time raise HDL levels?

When looking at how to raise HDL levels McTaggart & Jones (2008) points out that

Statins are effective in raising HDL-C in mixed hyperlipidemia, metabolic syndrome, and T2D, but this seems to be dependent on baseline parameters. Statins are less effective than fibrates in raising HDL-C in these conditions but achieve much greater LDL-C reductions. The evidence suggests that combination of a statin with a fibrate may provide benefits both on LDL and on the TG-HDL axis.

If this vastly increases the length of the answer I need to ask this in a separate question. Please advise me in the comments of that, but Wikipedia says that fibrates are a class of amphipathic carboxylic acids. Does this mean that fibrates are a pharmaceutical version of dietary fibre (complex [often large] carbohydrates)? If so, is introducing more fibre into your diet going to raise HDL levels?

References

McTaggart, F., & Jones, P. (2008). Effects of statins on high-density lipoproteins: a potential contribution to cardiovascular benefit. Cardiovascular drugs and therapy, 22(4), 321–338. PMC2493531 or https://doi.org/10.1007/s10557-008-6113-z