If your former position and experience is as specialized as you say, then future employers in the industry should understand that there are certain aspects of your former position you cannot divulge. Without more information about your specific situation I cannot be more detailed. Keep in mind that your NDA only covers "confidential" information, it generally does not apply to industry standard information.
Your NDA most likely only covers confidential information. A broad, high-level description of your experience that does not reveal any specific or proprietary information is probably safe to put on your résumé, but it would be wise to have a local business attorney review the agreement to determine just exactly what is and is not prohibited in order to avoid any pitfalls or potential litigation. Do keep in mind that an NDA typically covers all manners of disclosure, so waiting until the job interview to discuss the details you left off of your résumé will also be off-limits.
A common issue in such situations and actually it is generally quite solvable. I would give a local attorney such as Attorney Sloan, as he is in your city, a telephone call and make an appointment to have him advise you through, and around, the potential landmines.
No information provided in response to these questions can be relied upon in any way without further personally consulting with Attorney Kerrigan and Attorney Kerrigan consulting personally with you regarding your specific legal situation.