First pinpoint the location of the leak. American Leak Detection, or a similar company, has the equipment to do this. Some plumbers can do it.
I have seen it done, and it involves a transmitter on the end of the snake that goes through the drain line until it reaches the blockage. Then a handheld receiving device finds the location of the transmitter on the end of the snake, and that is where the blockage is located.
I think Xactimate has a unit cost to "camera a drain line". I think it is about $250 or so in Xactimate, but it costs about $350 minimum in my area.
The location procedure will determine if the blockage is in the yard under dirt, or if it is under a driveway or patio slab, or under a tree, etc, etc. Assuming it is in the yard, out in the open, the cost to repair will be whatever a plumber will charge to dig down by hand to reach the drain line, and then repair the drain line, and backfill the hole. If its not under a slab, I don't think any special equipment will be needed to make the repair.
Figure a two man plumbing crew will take all day (8 hours each man) to make the repair after the blockage is pinpointed, plus equipment, plus material. Whatever the plumber's labor rate is, plus truck charge, plus the material to make the repair will be a good starting point for an initial estimate.
After the blockage is located, you can bet the plumber won't have the proper pipe on his truck to make the repair, so he will have to go to the supply house to get it, which should be included in the 8 hours.
Once the blockage is located, a snake should be run down the rest of the drain line to make sure there isn't another blockage down line from the first blockage.
I have seen this procedure take two full days on a complicated drain system, so the above is just a starting suggestion.
Good Luck!