unwanted small. dense roots

I don't understand what is not safe about clumps of roots? The roots will either sprout new life or die and be feed for soil life. If you want to help the soil life digest the roots quicker, you could use enzymatic products that are sold just for this purpose, but they are generally used only in pots. When improving the soil, you would need to know what you are improving, so what is there, and what is missing. Is it heavy soil rich in clay? Then adding aeration in the form of compost can help. Is the soil very poor and very quick to dry out? Add clay AND compost. Have you grown plants with a lot of burnt spots on it? Maybe a spoonful of chalk lighlty powdered over the surface before rainfall can help. Lack of luster and very light green leaves? Throw a cup of kieserite on it! Working it in can be done, but is not always needed. Worms and rain will work it in on their own, but if your garden is very poor, it might be very beneficial to work it in. Plants and animals will feed the soil in the wild by dropping leaves and excrements, but we tend to take that away in an effort to take care of our gardens, so we must also add it back in, either yearly in a thin layer on top, or as one big load to work in all at once, or even better, start with the latter and manage every few years with the first. When plants die back at the end of the season you can sow in a green fertilizer like alfalfa to keep the soil occupied, and the alfalfa will serve as soil food when it reaches it's end of life. What are you planning to grow if I may ask?