Texture coordinate discontinuity with mipmaps creates seams

Texture coordinate discontinuity with mipmaps creates seams

I just started learning openGL and I am getting this artifact when texturing a sphere with mipmaps. Basically when the fragment samples the edge of my texture, it detects the discontinuity (say from 1 to 0) and picks the smallest mipmap, which creates this ugly seam:

So I tried to manually override the gradients using textureGrad:
//fragVert is the original vertex from the vertex shader
vec2 ll = vec2((atan(fragVert.y, fragVert.x) / 3.1415926 + 1.0) * 0.5, (asin(fragVert.z) / 3.1415926 + 0.5));
vec2 ll2 = ll;
if (ll.x < 0.01 || ll.x > 0.99)
    ll2.x = .5;
vec4 surfaceColor = textureGrad(material.tex, ll, dFdx(ll2), dFdy(ll2));
Now I get two seams instead of one. How can I get rid of them? And why does the code above generate 2 seams?

You can't tell from the two images but the 2 seams are on either side of the original seam.