In Mathematica, any version, Plot3D wants an expression or function giving z values as a function of x and y coordinates so... turn x+z==0 into x==-z into -(x+0*y)==z (or just plot -x) and now you have a function giving z values to plot.
In[1]:= Plot3D[-(x + 0*y) (*==z*), {x, -3, 3}, {y, -4, 4}]
Out[1]= ...PlotSnipped...
Carefully check some points on the surface to verify this is correct.
And, if you don't already know... this ---> (*==z*) <--- is a comment in Mathematica code.