Find a directory with a prefix in name

I have one big directory, that contains many subdirectories whose names are staring with 13xxx,10xxx,11xxx and so on. These directories contains text files with a name my_file.txt. Now the problem is, I want to change the files in the directories 13xxx and 11xxx only and don't want to touch files in 10xxx directories. I am trying to search directories with:

[ -d "13*"] && ..
[ -d "13"*] && ..

But seems like it doesn't work like this. Can anyone provide a small code that solves this riddle?

You can use a for-loop and globbing like:

for d in 1[13]*; do
    do_something "$d/my_file.txt";
done

or

for f in 1[13]*/my_file.txt; do
    do_something "$f";
done

So the answer was :

for d in 11*/; do
    echo "#Text to be added" >> "$d"/my_file.txt;
done
for d in 13*/; do
    echo "#Text to be added" >> "$d"/my_file.txt;
done