My friend recently gave me a potted mint plant, but since I got it, the leaves have been dying. I saw that "rust" fungus is a common issue on mint plants, but mine does not appear to have any rust spots.

Here are the Symptoms:
* Leaf tips on leaves, especially older leaves turning black. Eventually, the entire leaf dries up and I pull it off.
* Lateral buds seem to be in many cases turning black and dying before even becoming 1mm in length - barely visible if not contrasted against the green of the plant.

Is there any way for me to save this plant?