In the state of NC is a salaried employee e titled to overtime pay if they work 55-65 hours a week

The issue of salary versus hourly is of little importance when faced with an overtime question. An employee in North Carolina must be paid for all hours worked over 40 per week unless the employee is an exempt employee.  There are about a half a dozen different exemptions.  If you fall in one of the exemptions, then it does not matter if you work 40 hours, 50 hours, 100 hours or more, you are not entitled to overtime. If you have questions about whether you are exempt or not, you should consult with an experienced employment attorney.