`x^3+y^3-6xy=-11`

`(x+y)^3-3xy(x+y)-6xy=-11`

`(x+y)^3-3xy(x+y+2)+11=0`

`(x+y)^3+8-3xy(x+y+2)+3=0`

`(x+y+2)(x^2+2xy+y^2-2x-2y+4)-3xy(x+y+2)+3=0`

`(x+y+2)(x^2-xy+y^2-2x-2y+4)+3=0` 

`x+y+2=-3/(x^2-xy+y^2-2x-2y+4)`

`x+y+2=-6/(2x^2-2xy+2y^2-4x-4y+8)`

`x+y+2=-6/((x^2-2xy+y^2)+(x^2-4x+4)+(y^2-4x+4))`

`x+y+2=-6/((x-y)^2+(x-2)^2+(y-2)^2)`

Ta có: `(x-y)^2+(x-2)^2+(y-2)^2>=0`

Mà: `(x-y)^2+(x-2)^2+(y-2)^2\ne0`

Suy ra: `(x-y)^2+(x-2)^2+(y-2)^2>0`

`->-6/((x-y)^2+(x-2)^2+(y-2)^2)<0`

Hay: `x+y+2<0`

Suy ra: `x+y<-2`  

Giả sử: `x+y<=-7/3`

`->x<=-7/3-y`

`->x^3+y^3-6xy<=(-7/3-y)^3+y^3-6(-7/3-y)y`

`=-(7/3+y)^3+y^3+6(7/3+y)y`

`=-343/27-49/3y-7y^2-y^3+y^3+14y+6y^2`

`=-343/27-7/3y-y^2`

`=-y^2-7/3y-343/27` 

Suy ra: `-11<=-y^2-7/3y-343/27`

`y^2-7/3y+343/27<=11`

`y^2-7/3+343/27-11<=0`

`y^2-7/3x+46/27<=0` 

`(y-7/6)^2+37/108<=0` 

Mà: `(y-7/6)^2+37/108>=37/108>0\AAy`

Do đó mâu thuẫn 

Suy ra: `x+y<=-7/3` (sai)

`->x+y> -7/3`

vậy: `-7/3<x+y<-2`