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I have recently obtained a locked briefcase by, uhm, completely legal means.

Stop looking at me like that.

The combination lock has six numbers and I can't seem to figure out the correct combination. There was a small note attached. Maybe it's the owner's favourite poem or something? Seems like near-gibberish to me, though.

Nine must take gṛeat carẹ w$h$en oṗ$e$ning this box;
Only th$r$ee shạ$r$p mịnds $i$ts secṛet u$n$locks.
Have a $g$o aṭ tḥi$s$ rhymẹ,
Iṇ fact yoụ still have tiṃe.
Not yet tool one to decode these text ḅlocks.

Tre$a$sure awaiting $b$e two puzzled eyes;
Having five find $o$ut the tr$u$th from the lies.
Examine evẹry li$n$e,
Refactor, ṛe$d$efine,
Eagerly ṣevening in on the prize.

What I've tried:

931-257

Wasn't it... shucks. Out of ideas now.

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As stated by Hunter in his answer, there are many red herrings but one true clue:

the dotted letters read: REPAIR THE NUMBERS

So let's follow that advice and fix the text accordingly:

Nine ONE must take gṛeat carẹ when oṗening this box;
Only three TWO (to) shạrp mịnds its secṛet unlocks.
Have a go aṭ tḥis rhymẹ,
Iṇ fact yoụ still have tiṃe.
Not yet tool one EIGHT (too late) to decode these text ḅlocks.

Treasure awaiting be two FOUR (before) puzzled eyes;
Having five TWO (to) find out the truth from the lies.
Examine evẹry line,
Refactor, ṛedefine,
Eagerly ṣeven ZEROing in on the prize.

This gives us the true six-digit code:

128420 (thanks to @MOehm for correcting me)

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    $\begingroup$ Very good, but I think that rot13(gbby bar orpbzrf gbby rvtug be gbb yngr naq, creuncf, friravat va orpbzrf mrebvat va). $\endgroup$ – M Oehm Aug 7 '18 at 12:54
  • $\begingroup$ @MOehm, I was just going to answer the same thing :) $\endgroup$ – OfFPiR Aug 7 '18 at 13:00
  • $\begingroup$ Thank you @MOehm, that seems more logical indeed. Fixing my answer. $\endgroup$ – xhienne Aug 7 '18 at 13:11
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Partial answer

Taking the first letter of each line you find:

NO HINT HERE (a red herring...)

The letters in italic font spell:

HERRINGS ABOUND (another red herring...)

While taking al the letters with small dots under and over them you read:

REPAIR THE NUMBERS (maybe a useful hint, this time?)

Still working on it...

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