(Nivo Slider v3.2) This is a proper slide effect that slides an image in from the left (and is visually analogous to the 'slideInRight' effect), and doesn't depend on the outer slider and wrapper having overflow:hidden.

gistfile1.txt

... effects if/else if block ...
} else if(currentEffect === 'slideInFromLeft'){
    createSlices(slider, settings, vars);
        
    firstSlice = $('.nivo-slice:first', slider);
    firstSlice.css({
        'width': '0px',
        'left' : '0px',
        'right': '',
        'opacity': '1'
    });

    firstSlice.children('img').css({
        'left': 'auto',
        'right': '0'
    });

    firstSlice.animate({ width: slider.width() + 'px' }, (settings.animSpeed*2), '', function(){ 
        // Reset positioning
        firstSlice.css({
            'left': '-0px',
            'right': ''
        });
        slider.trigger('nivo:animFinished'); 
        firstSlice.children('img').css({
            'right': 'auto',
            'left' : ''
        });
    });
} 
... effects if/else if block continued...