We do not recommend that you continue to use an outdated version of Firefox, as these versions may contain security or functionality issues. Mozilla is not responsible to adjusting the compatibility of an addon and it is the developer's duty to make any required changes to get the addon to function properly on newer versions of Firefox. Please contact the developer of that addon about the issue and they may update it.

It is not Firefox that is made compatible with IDM and the many other plugins and Extensions out there but the other way.

from http://www.internetdownloadmanager.com/register/new_faq/bi21.html

   FireFox Browser Integration
   I have problem with IDM integration in FireFox 30,31,32,33 and 34. What should I do?

   Download and install the latest version. It supports FireFox 30,31,32,33 and 34. If it does not help, please read this instruction.