Find the value of $x$ in the diagram below.

[asy]
size( 200 ) ;

pair ll = origin ;
pair lr = origin+dir(0) ;
pair ul = extension( ll,ll+dir(90) , lr,lr+dir(120) ) ;
pair ur = extension( ul,ul+dir(0) , lr,lr+dir(30) ) ;

draw( ll--lr--ur--ul--cycle ) ;
draw(rightanglemark( lr,ll,ul, 7 )) ;
draw(rightanglemark( ll,ul,ur, 7 )) ;

draw( lr--ul , dashed ) ;
draw(rightanglemark(ur,lr,ul , 7 )) ;

label( "$1$" , ll--lr , S ) ;
label( "$x$" , ul--ur , N ) ;
label( "$60^{\circ}$" , lr , 2.5dir(155) ) ;
[/asy]