What is the most energy efficient way to get rid of ice dams on a slate roof? The roofer suggests heating cables. Isn't there a better way?

We have a brick Tudor house with a slate roof in Massachusetts. I've been told that the heating cables have to be left on all winter. Someone else suggested a ridge vent and soffit vents. We have blown in cellulose insulation in the attic. Would this block the soffit vents? We also have an attic fan which cools the house nicely on summer evenings. Would the ridge vent negate the value of the ridge vent? The worst ice dam is over our front door where the icicles then melt onto the landing which then becomes a sheet of ice. Do we need to insulate the underside of the roof?