You didn't mention what species you are interested in but between 11 states and usually 5-6 species per state, that is a boatload of fees if you're really going to apply for them all. I think you'll find you need much deeper pockets than you think, especially since some states want license and tag fees upfront and in some states license costs are nonrefundable if you want to store up bonus points.
Some states are not worth applying in because the number of nonresident tags is too small, draw odds are too low, points needed will take you decades to accumulate or a host of other reasons. You need to do a good bit of research first.
I would definitely at least talk to a booking agent as HT suggested. I would also use the Members Research Section (MRS) found in the two Eastmans' magazines. It pulls a tremendous amount of information together for you and will save you a ton of time on what is going to be a huge undertaking, much bigger than you realize.
Call Eastmans' at (800)842-6887 and tell them you want to subscribe to both the Eastmans' Hunting Journal and Eastmans' Bowhunting Journal. Start your Eastmans' subscription with the recent issue that has the first cross-state MRS in it. That will help you narrow down the states. Then, look at the individual state MRSs each month.
The only problem you will have is that some states have application deadlines before the MRS is published for other states with later deadlines. To get around that, you can download MRSs from last year on the Eastmans' web site once you are a subscriber.
Honestly though, you won't be able to get through all this before you need to start applying. So, use a booking agent the first year or pick your states to apply for based on the two cross-state MRSs that are already out. In the first year, except in the random draw states, apply for preference and bonus points rather than specific hunts.
Don't rush. You'll waste a lot of money on states you won't apply for again once you know more. Don't apply in more than 3-4 states per species. Skip mountain goat and down the road hunt them in BC or Alaska.