This is a question that arises in many different ways and I am reluctant to give my opinion because when it comes to food and what to eat there is an infinite number of answers. Hopinso has just answered a similar question:
You need a good variety of fresh and unadulterated food. Beans have their place and the theory proffered on the link you provided is fine. Also good are green vegetables, root vegetables, oats and fruit like gooseberries, blackcurrants rhubarb and of course the apple. There is also loads of other things that I haven't mentioned or don't know about and a variety is essential. All these foods are all able to assist in the circulation of cholesterol through the bile and expel it forcing new bile to be created and there buy establishing a strong biliary cycle. These natural foods also contain the nutrients to nourish and maintain the liver in good condition. Organic and unadulterated is best.
I am not sure whether eating beans or anything else actually fully dissolves stones. Dissolving stones particularly large ones would appear to take a long time (possibly years). Flushing gets the biliary system clear but it needs to be accompanied by life changes like changing your diet, taking exercise, etc.