#Ruby, 150 bytes

All the string formatting abuse!!!

Credit for formula obtaining the last number goes to @xnor here.

u=1+rand(6)
l=([*1..6]-[u,u^7]).sample
$><<'%11s
 /\%8s
 / \%4d%4s
{ %d }%s}
 \ /%4d%4s
 \/%s/'%[?_*8,?\,円u,?\,円l,?-*7,3*u*l*(u*u-l*l)%7,?/,?_*7]

Ruby, 150 bytes

All the string formatting abuse!!!

Credit for formula obtaining the last number goes to @xnor here.

u=1+rand(6)
l=([*1..6]-[u,u^7]).sample
$><<'%11s
 /\%8s
 / \%4d%4s
{ %d }%s}
 \ /%4d%4s
 \/%s/'%[?_*8,?\,円u,?\,円l,?-*7,3*u*l*(u*u-l*l)%7,?/,?_*7]

#Ruby, 150 bytes

All the string formatting abuse!!!

Credit for formula obtaining the last number goes to @xnor here.

u=1+rand(6)
l=([*1..6]-[u,u^7]).sample
$><<'%11s
 /\%8s
 / \%4d%4s
{ %d }%s}
 \ /%4d%4s
 \/%s/'%[?_*8,?\,円u,?\,円l,?-*7,3*u*l*(u*u-l*l)%7,?/,?_*7]

#Ruby, 150 bytes

All the string formatting abuse!!!

Credit for formula obtaining the last number goes to @xnor here.

u=1+rand(6)
l=([*1..6]-[u,u^7]).sample
$><<'%11s
 /\%8s
 / \%4d%4s
{ %d }%s}
 \ /%4d%4s
 \/%s/'%[?_*8,?\,円u,?\,円l,?-*7,3*u*l*(u*u-l*l)%7,?/,?_*7]

#Ruby, 150 bytes

All the string formatting abuse!!!

Credit for formula obtaining the last number goes to @JonathanAllan

u=1+rand(6)
l=([*1..6]-[u,u^7]).sample
$><<'%11s
 /\%8s
 / \%4d%4s
{ %d }%s}
 \ /%4d%4s
 \/%s/'%[?_*8,?\,円u,?\,円l,?-*7,3*u*l*(u*u-l*l)%7,?/,?_*7]

#Ruby, 150 bytes

All the string formatting abuse!!!

Credit for formula obtaining the last number goes to @xnor here .

u=1+rand(6)
l=([*1..6]-[u,u^7]).sample
$><<'%11s
 /\%8s
 / \%4d%4s
{ %d }%s}
 \ /%4d%4s
 \/%s/'%[?_*8,?\,円u,?\,円l,?-*7,3*u*l*(u*u-l*l)%7,?/,?_*7]