This puzzle is part of the Monthly Topic Challenge #13: Variety Slitherlinks.
The final answer is a six letter word.
Prefer no partial answers.
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The slithelink seems to be impossible. To fix that issue you need to ...
Ignore the green lines. They are not part of the solution.
If you do that and you use the fact that green lines are not part of the path, you can solve the slitherlink.
Look at the green rectangles, look at the lines in and bordering these rectanges, including the original green lines, they spell "PIGPEn".
Pigpen is a traditional cipher that encodes the alphabet in partially drawn squares. Possibly with a dot in the center.
Notice that some of the yellow squares contain a dot. The lines bordering the yellow squares with the dots form pigpen letters. They spell "DIALPAD".
The red squares seem to use a similar code as the yellow squares. But they spell "DDAIFH". Not very convincing.
If you replace the "hash" figure of the pigpen alphabet with a dialpad, you get 441968. Or, if you read the corresponding letters,
If I take 1 as a space, I can make up "HI YOU".
Unfortunately that is not a 6-letter word. A 6-character solution at most. Even so, the answer "hi, you!" looks a bit awkward. So, well, I must be missing something.
There are variations on the letters on dialpads with letters on the 1 key but I couldn't find one that yields a meaningful word.
Update and conclusion
The title "An X x X Slitherlink related to X" means a 10x10 slitherlink. But stresses that the solution has to do with X somehow.
Stiv noted that
441968 could be a date, 4.4.1968, which happens to be the date of Marting Luther King's assassination. He ventures the X is then a reference to Malcolm X. While this is intriguing, it ends up being a coincidence.
Then SeptaCube cracked the last step:
"If you just consider the number of surrounding segments [of the red cells] you can get 332233, which uniquely translates to DECADE [on a dialpad]."
X is 10 in roman numerals, referring to the 10 years in a decade.
This solution was confirmed by the Puzzle setter.