/ --> \/

If I where you I'd change delimiter and try m{REGEX} instead of m/REGEX/ .

update

there where more issues, but this works for me ( perl -dE0 starts the debugger )

  DB<25> @m =  qw{01/LC-13/E10GbE-1 01/LC-13/E10GbE-1,01/LC-14/E10GbE-
+1}

  DB<26> say join ":", m{\d\d/\w+-(\d+)/\w+-(\d+),?}g for @m
13:1
13:1:14:1

  DB<27>
[download]

update

If the snippets don't always start with \d\d change it to \d+

If I where you I'd consider spliting on , and then / .

Then applying a simple regex, should be more stable and maintainable.