3D ASCII Block Building
C,  376   350   313   309  285 bytes

Thanks to @Jonathan Frech for saving four bytes!



#define F for(
char*t,G[26][67],*s;i,j,e,k,v,x,y;b(){F s="\\/__//\\__\\ ___ ";*s;--y,s+=5)F e=5;e--;*t=*s&lt;33&amp;*t&gt;32?*t:s[e])t=G[y]+x+e;}f(int*M){F;e&lt;1716;++e)G[e/66][e%66]=32;F k=0;++k&lt;12;)F i=0;i&lt;11;++i)F j=11;j--;v+k||b())x=i+j*3+k,y=14+i-k,(v=M[i*11+j])&gt;=k&amp;&amp;b();F;++e&lt;26;)puts(G+e);}


Try it online!

Unrolled:

#define F for(

char *t, G[26][67], *s;
i, j, e, k, v, x, y;

b()
{
    F s="\\/__//\\__\\ ___ "; *s; --y, s+=5)
        F e=5; e--; *t=*s&lt;33&amp;*t&gt;32?*t:s[e])
            t = G[y]+x+e;
}

f(int*M)
{
    F; e&lt;1716; ++e)
        G[e/66][e%66] = 32;

    F k=0; ++k&lt;12;)
        F i=0; i&lt;11; ++i)
            F j=11; j--; v+k||b())
                x = i+j*3+k,
                y = 14+i-k,
                (v=M[i*11+j])&gt;=k &amp;&amp; b();

    F; ++e&lt;26;)
        puts(G+e);
}