Use find command to select directories with a file type

I am using

find $dir -type d|grep -i $word

to retrieve a list of directories, case-insesnsitive, that contain word "TEST" in it's path.

Now I'd like to modify it to only retrieve those directories that contain files of type .txt

how can i accomplish that?
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Like this:

find $dir -type d|grep -i $word |while read DIR
    if ls $DIR/*.txt >/dev/null 2>&1
         echo $DIR

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perl -MFile::Find -le 'find {wanted=>sub{print if -d && /'$word'/ && <$_/*.txt>},no_chdir=>1},shift;' $dir
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