Unfortunately, you will probably need a new rear wheel (or at least a new rear hub). In the 2005 era, the width between the flanges were as wide as possible while still accommodating the width of an 8/9/10 speed Shimano freehub. The 11-speed road cassette requires a wider freehub, and with very few exceptions, there is no ability to swap in the wider freehub on an 8/9/10-speed era rear hub.
One notable exception to this era were Mavic wheels. These had a wider freehub to accommodate a specific Campy(?) cassette, and in a somewhat prophetic stroke of luck, these old Mavic hubs would take an 11-speed cassette. Just remove the additional spacer and go 11-speed (I actually did this with a set of Mavic Ksyrium wheels that I bought back in the early 2000’s).
There is one option to purchasing a new rear wheel/hub. The Shimano 11-34 (11-speed) cassette (CS-HG8000-11) is an Ultegra-branded item that is compatible with the 8/9/10 speed freehub you have. The 11-34 comes with a spacer (that you would not use) to fit on the wider 11-speed freehub. You are limited to that one cassette however. The 11-32 and smaller need the 11-speed freehub. ALSO, you would require the longer cage rear derailleur to work with the 11-34 cassette. It would be the RD-R8000-GS I believe (the -SS is the shorter cage that would not have the capacity for the 11-34). The RD-R8000-GS is usable down to an 11-28 11-speed cassette if in the future you were to invest in a new wheelset that has an 11-speed freehub.
SHIMANO - 11-Speed - HG-EV - 11-34T Road Cassette Sprocket
SHIMANO ULTEGRA - Rear Derailleur - Medium Cage - SHIMANO SHADOW RD - 11-speed