Is the answer...
SCOTCH PIE ?
I arrived at this answer as follows:
In the lefthand grid, after the 22 squares are shaded, combine the remaining numbers with the corresponding 'L' or 'R' indicators on the right grid, to get the image below.
Step through each row, summing the total or L's and R's in the row to arrive at a single number.
For example, in the first row, we have 7L 6R 4L 5L 1R 8R. This adds up to 1L.
Doing this for each row, we get 1L 9R 3R 11L 19R 8R 23R 26R 14L. Now apply each of those as a Caesar shift to the corresponding ciphertext letter. For example, the first letter in the ciphertext (which, as we were told, applies to the first row) is D. If enciphering, we shift 1L to C, but if deciphering, we shift 1R to E.
Using this method for each character in DXFDMKEPU, we get EOCSTCHPI as the deciphered text. This anagrams to SCOTCH PIE.
The solution to the lefthand grid is as follows. Note that BeastlyGerbil was the first to complete this grid.
First, note the column with three adjacent 2's. If the middle of these were shaded, the other two could not be, and there would be redundant 2's in the column. So the middle 2 CANNOT be shaded, and other two MUST be shaded, to avoid redundancy. Also, because the middle 2 is not shaded, the other 2 in its row MUST be shaded.
No square adjacent to a shaded square can, itself, be shaded, as that would violate the puzzle rules. So none of the 7s adjacent to the upper shaded 2, the 1 adjacent to the lower shaded 2, or the 4 adjacent to the righthand shaded 2 can themselves be shaded. Therefore, we can shade all of the identical numbers in the same columns and rows as these unshaded numbers.
Using the same reasoning, additional protected (cannot be shaded) squares are: the 5 directly above the rightmost shaded 2 and the 6 directly below the rightmost shaded 1. The other identical numbers in the same columns must be shaded. Once this is done, we can also shade a 4 at the top and 5 on the right, using the same reasoning.
Now we can go through the whole grid, row-by-row and column-by-column, looking for two or more of the same digit. If found, and if one of these digits is immediately adjacent to a shaded square, we know that it cannot be shaded, but the other must be shaded. Doing that, the grid now looks like this:
Two repeated numbers are still in the grid: two 7s in the second row, and two 3s in the 9th column. We can use another rule to determine which to shade. In each case, shading a particular one of the 7s and one of the 3s would result in a single isolated white square, which does not connect with the rest of the grid. This violates the puzzle rules, so the OTHER of these two squares must be shaded. Doing so, we get the final grid: