  We present a technique that can be used to generate a static, axisymmetric
solution of the Einstein-Maxwell-Dilaton equations from a stationary,
axisymmetric solution of the vacuum Einstein equations. Starting from the Kerr
solution, Davidson and Gedalin have previously made use of this technique to
obtain a pair of oppositely charged, extremal dilatonic black holes, known as a
black dihole. In this paper, we shall instead start from the Kerr-NUT solution.
It will be shown that the new solution can also be interpreted as a dihole, but
with the black holes carrying unbalanced magnetic charges. The effect of the
NUT-parameter is to introduce a net magnetic charge into the system. Finally,
we uplift our solution to ten dimensions to describe a system consisting of D6
and anti-D6-branes with unbalanced charges. The limit in which they coincide
agrees with a solution recently derived by Brax et al..
