Note: your basic info sidebar says L3301. I assume that is the tractor you want to put this cutter on. (??) NO! Sorry I missed the L6060 in the post title. I'll edit out the smaller machine comments below...
I run a 7'8" flail (that does not go out to the side like the one you are considering) and I use an 81 hp MF to drive it. I think your L6060 will handle this Titan cutter very well.
If you go to the Titan website (using the link you gave us) and then click on the box with mower width (like 65") , then go to the fine print of the Product Overview that specifies min and max HP they recommend. If you go down to the Specs it disagrees with itself and says "30 to 50 hp." Like anything else you buy, it is really important in my view to go talk to someone who owns one. The dealer should point you to other customers and if he has none yet then Titan should give you some leads. On-line comments are nice but they do not cut it...so to speak.
Titan is not very careful with their specs. For example if you have the 57 inch model selected the very same table of specs says Min Power 30 hp on the left and on the right says Power Required 25-50hp. Nowhere that I can see do they state the weight of the attachment. I am distrustful enough of Titan that I would go see whether this is a machine they made to begin with , whether they bought someone out and what the history of the line if cutters is.
Looks to me like a very useful cutter to have around. An impressive looking mower on paper and should be really nice for people with ditches and banks, etc. not requiring the reach of a big long armed "articulated arm" public roads style machine. I think the off balance side load is going to give you some grief at times if you go too big. You may want to consider "Y" type blades vs the heavier forged chopper style blades. The "Y" type are not good for woody stuff, thick branches, seedlings, etc. but great for weeds, briars, heavy grass, etc.
By the way, it depends a lot on what you need to cut. If you only have weeds and grass, with no saplings or woody stuff, you can get several brands of sickle bar cutters a lot less expensive and with much less cantilevered weight out to the side if you have need to reach further.
