You're going to have to spend hundreds on parts.

At a minimum, 5800 levers, 5800 cassette, 5800 RD and 11-speed chain (KMC might have less expensive options than Shimano). Don't know how your chainrings will play with the 11-speed chain, but they might might need to be changed, too (or a whole new crankset). Cable pull between the new levers and existing brakes will probably not be ideal, either.

New, from UK vendors, these are all pretty reasonably priced, IMO, but it's still going to add up to more than $200. Hunting for used stuff might save you a little bit of money, but I doubt it'll move the needle very much.