Total hyphenation

InDesign has hyphenation rules for lots of languages, but unfortunately not one for "Music" (although it is often called "the universal language"). But: despite what you think – because you see it on your screen –, this 'is' not music. This is a random selection of symbols whose font is to display them as music notes. So even if InDesign had an option to intelligently break such lines, it would not work with such a font anyway. (A-tonal as I am, I am in the dark on how such an hyphenation algorithm might work – based on rhythm? rhyme? meter?)

Yet not all is lost. You don't want "hyphenation" because that would introduce a visible hyphen at the end of each line. And probably the hyphen looks like a note or clef or bass anyway -- you wouldn't want any random character to pop up either. But InDesign can also break a line without showing a hyphen! Manually insert a Discretionary Break at a reasonable place and InDesign will use it as a breaking point as if there is a regular space there. No worries if it does not, because if it's not "in use", it will be invisible (come to think of it, it's also invisible when in use).

If that works for you, you could either try to find a common pattern to break before or after and insert Discretionary Breaks through targeted Find and Change operations (and again, no worries if you have more than absolutely needed), or, if you cannot locate such patterns, assign a hotkey to the menu code and add it manually whereever you see it might be useful.

Well, I'm not sure what you mean by authorized but to turn hyphenation on, simply open the Paragraph panel or go to the Control panel and enable the hyphenate checkbox. Also a screen shot showing the hidden characters might help us to understand how the text is flowing.