Did i read correctly that dysplasias can develop into invasive cancer in less than a year? how does that imply a likely cure?

Yes: If not faster. There are a variety of subtypes of cervical dysplasia based on their likelihood of turning aggressive. The tamest pose no measurable risk if watched for some time. This is why it is so important to recognize and remove the dangerous ones.

Consistent follow-up: Majority of the dysplasias do not turn malignant, let alone in less than a year. However, since the risk of malignancy is higher with dysplasia, the condition deserves consistent follow-up, avoidance of carcinogens, like tobacco, taking diagnostic and therapeutic action, like pap smear, endoscopy, excision of suspicious areas and keeping in regular consultation with your doctor.