sudo dd if=./linuxmint-17.1-cinnamon-64bit.iso of=/dev/sdd bs=1M
You copied a file (image) to a device, not a partition - everything under the iso is hosed, the partition table has been rewritten. Why do they nick dd the data destroyer? beats me...
Anyway.... Linux conforms to the ntfs spec, so the backup table will be overwritten, also. What will remain are the old sector boundaries that have not actually been overwritten (by your iso or other) for all old partitions - TestDisk can find those using its sector search (Deeper Search).
You must recognise the valid from all that it finds, and write them to the table. Of course, the new partition sector will be the first valid one. Your searches can be quicker if all your partitions were written to cylinder boundaries (XP spec); if not necessarily so (Vista, W7 spec), then the search is quite slow.
Each boundary sector (there are beginning and end sectors) contains a table with beginning and end info for that partition, and the MFT location. You need those MFTs - without them, files are simply lost. Testdisk can read file tables, but not rebuild them. So if you choose an incorrect boundary then TD will likely not find that partition's FT (you test by checking file lists, contents).
When satisfied, you write the table. Not correct? Nothing more is lost, but time - you do it all again.
As for your OS, 1.4GB is a lot to lose; there is an excellent possibility that your FT ...