Let $$x,y,z$$ be positive real numbers such that $$x^2+y^2=49$$, $$y^2+yz+z^2=36$$ and $$x^2+\sqrt{3}xz+z^2=25$$. If the value of $$2xy+\sqrt{3}yz+xz$$ can be written as $$p\sqrt{q}$$ where $$p,q$$ are integers and $$q$$ is not divisible by the square of any prime, find $$p+q$$.