Try :
a = gca;
hold on
plot(a.XLim,[560, 560],'m--') % plots horizontal line at y = 560
To find the intersection point at y = 560 with the function data ('ydata' for example below)
indx = find((ydata-560).*([ydata(1),ydata(1:end-1)]-560)<0); % finds index corresponding to intersection points
num_of_intersection = length(indx)
xintersect = xdata(indx)
Let me know if there is any doubt
