Did reconstruction successfully solve the issue of division between the north and south?

The question of the restoration of the seceded states to the Union became an issue long before the surrender at Appomattox, Virginia, on 9 April 1865. According to the Crittenden-Johnson Resolutions of July 1861, the object of the war was to restore the Union with "all the dignity, equality, and rights of the several States unimpaired." But as the conflict progressed, it became evident that this objective was impossible to achieve. Congress refused to reaffirm its policy, President Abraham Lincoln appointed military governors for partially reconquered states, and moderate and radical Republicans debated the exact status of insurgent communities.

So they had to declare war to do so, so Yes