I have had success using the Quikchange methodology (see Agilent web site), but only with Pfu turbo, not with Phusion. If it doesn't work (your plasmid is fairly big), make two overlapping PCR fragments bearing the desired fragments, fuse them by PCR using the distal primers and reclone them in your vector.
I successfully used overlapping PCR to insert mutations in a sequence. You can make two fragments using standard PCR reactions and then fuse them using Overlap extension PCR. See the link http://link.springer.com/protocol/10.1007%2F978-1-60761-652-8_10
Rather than amplifying the entire 11 kb, you could use overlap PCR to create a smaller fragment (e.g., approximately 1-3 kb) that contains the mutation. Then use standard restriction digestion and subcloning to replace this fragment in your vector.