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<33&*t>32?*t:s[e])t=G[y]+x+e;}f(int*M){F;e<1716;++e)G[e/66][e%66]=32;F k=0;++k<12;)F i=0;i<11;++i)F j=11;j--;v+k||b())x=i+j*3+k,y=14+i-k,(v=M[i*11+j])>=k&&b();F;++e<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<33&*t>32?*t:s[e])
            t = G[y]+x+e;
}

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

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

    F; ++e<26;)
        puts(G+e);
}

Charcoal, 70 69 68 bytes

≔Ｅ¹¹⮌Ｉ⪪Ｓ,θＦ²Ｆ¹¹Ｆ¹¹Ｆ¹¹«Ｊ⁻⁻⁺λκ×μ³ι⁻λκ≔§§θλμη¿∨⁼±η⊕κ‹κη¿ι“↗⊟&⁹κＵhnI”___

Try it online! Link is to verbose version of code. Explanation:

≔Ｅ¹¹⮌Ｉ⪪Ｓ,θ

Read the array, split each line on commas and cast to integer, but also reverse each line, since we want to draw right-to-left so that left columns overwrite right columns. (Other dimensions already have desired overwriting behaviour.)

Ｆ²Ｆ¹¹Ｆ¹¹Ｆ¹¹«

Loop through i) top lines and bodies k) height l) rows m) columns. (Looping through first top lines and then bodies avoids overwriting bodies with top lines.)

Ｊ⁻⁻⁺λκ×μ³ι⁻λκ

Jump to the position of the cube.

≔§§θλμη

Fetch the height at the current row and column.

¿∨⁼±η⊕κ‹κη

Test whether a cube should be drawn at this height for this row and column.

¿ι“↗⊟&⁹κＵhnI”___

Draw the body or top of the cube.

JavaScript (ES6), 277 251 bytes

a=>(n=55,$=f=>[...Array(n)].map((_,i)=>f(i)),S=$(_=>$(_=>' ')),n=11,$(l=>$(z=>$(y=>$(x=>(x=10-x,X=x*3+y+z,Y=y-z+n,Z=a[y][x])<=z&&Z+z+1?0:l?['/\\__\\','\\/__/'].map(s=>S[++Y].splice(X,5,...s)):S[Y].splice(X+1,3,...'___'))))),S.map(r=>r.join``).join`
`)

f=

a=>(n=55,$=f=>[...Array(n)].map((_,i)=>f(i)),S=$(_=>$(_=>' ')),n=11,$(l=>$(z=>$(y=>$(x=>(x=10-x,X=x*3+y+z,Y=y-z+n,Z=a[y][x])<=z&&Z+z+1?0:l?['/\\__\\','\\/__/'].map(s=>S[++Y].splice(X,5,...s)):S[Y].splice(X+1,3,...'___'))))),S.map(r=>r.join``).join`
`)

console.log(f([
	[3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11],
	[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
	[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
	[1, 0, 0, 7,-7,-7,-7,-7, 7, 0, 0],
	[0, 0, 0, 7,-7,-7,-7,-7, 7, 0, 0],
	[0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0],
	[0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0],
	[1, 0, 0, 4, 3, 2, 1, 0, 0, 0, 1],
	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
	[1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 11]
]))

Saved 26 bytes from @Neil's suggestion.

Ungolfed

a=>(
    n=55,
    $=f=>[...Array(n)].map((_,i)=>f(i)),
    S=$(_=>$(_=>' ')),
    n=11,
    $(l=>
        $(z=>$(y=>$(x=>(
            x=10-x,
            X=x*3+y+z,
            Y=y-z+n,
            Z=a[y][x],
            Z<=z && Z+z+1 || (
                l
                ? ['/\\__\\','\\/__/'].map(s=>S[++Y].splice(X,5,...s))
                : S[Y].splice(X+1,3,...'___')
            )
        ))))
    ),
    S.map(r=>r.join``).join`\n`
)